Katalog me pune laboratori

PHYSICSL A B O R ATO RY E X P E R I M E N TS

New Experiments

Ripple Tank page 51

Plasma Physics page 239

X-rays of Tungsten page 263

X-ray Energy Detector page 264

Vorspann 09.08.2007 12:53 Uhr Seite 1111

Dear customer,

this catalogue of physics laboratory experiments for universities, colleges, high schools etc. is a valuable and

extensive work of scientific literature for experiment-oriented education purposes. It includes numerous successful

and classical experiments playing an essential role in every physics laboratory course. The experiments have been

field-tested over and over again and countless enthusiastic customers all over the world have been inspired

by them.

Our team of experienced scientists has set great store on using both classical equipment, such as oscilloscopes,

recorders etc., and modern interface systems like our Cobra3 system for the experiments. This is why you will often

find several versions for one experiment. Just choose the experiment version which best meets your specific

requirements.

If you need help in selecting the right experiments, our sales representatives in your country would be more than

happy to assist you.

We hope you enjoy our manual and look forward to your questions.

Phywe Systeme GmbH & Co. KG

PHYWE Systeme GmbH & Co. KG

Robert-Bosch-Breite 10

D-37079 Göttingen · Germany

Phone + 49/551/604- 0

Fax + 49/551/604 -115

www.phywe.com

[email protected]


1

About Phywe

Founded in Göttingen, Germany in 1913 by Dr. Gotthelf Leimbach, Phywe Systeme GmbH & Co. KG quickly advanced

to one of the leading manufacturers of scientific equipment.

Over this period of more than 90 years Phywe has been putting quality and innovation into its products as a

fundamental requirement.

As a well known international supplier in the fields of science and engineering we have made a significant impact on

the market through high quality equipment.

Phywe products are made in Germany and in use throughout the world in the fields of education und research, from

primary schools right through to university level.

Up-to-date educational systems, planning and commissioning of scientific and engineering laboratories to meet

specific requirements are our daily business.

As a supplier of complete, fully developed and established systems, Phywe provides teaching and learning systems

for students as well as teacher demonstration experiments. The system ranges from simple, easy to operate

equipment intended for student use up to coverage of highly sophisticated and specialised university equipment

demands.

Phywe Systeme GmbH & Co. KG has achieved a very high standard based on research and technology and through

exchange of experiences with universities and high schools as well as with professors and teachers.

As experienced and competent manufacturer, we would gladly assist you in the

selection of the "right" experiments for your particular curricula.


2

Mechanics Measurement techniques Phywe in the University City of Göttingen –

Natural sciences have a longstanding

tradition in Göttingen. More than 40 Nobel

prizewinners coming from all areas of

scientific disciplines and numerous university

institutes successfully conduct research in

practically all areas of science.

The following research institutions and

university institutes are located in Göttingen:

Academy of Science, several Max-Planck

institutes, the German Primate Centre, the

Centre of Molecular Physiology of the Brain,

the Centre of Molecular Life Science –

to name just a few.

We are in contact with these institutions and

exchange our views with them to ensure that

the latest trends and scientific innovations

are always reflected in the product range of

Phywe Systeme GmbH & Co. KG.


3

A Center of Natural Sciences in Germany

GÖTTINGEN is a city of teaching and research. Scientific equipment, teaching

equipment and laboratory installations developed and produced in this city are famous

throughout the world.

Göttingen would not be what it is without its university.

“Georgia Augusta” was founded in 1734 and by 1777 it was Germany‘s largest

university, with 700 students. It still is one of the leading universities in Germany, with

14 faculties, significant scientific facilities and more than 30,000 students.

The gracious Goose Girl (“Gänseliesel”) on the market place well is the most kissed girl

in Germany. Why? Because every newly graduated doctor must kiss the cold beauty on

her bronze mouth. That is Göttingen tradition.

Doctor’s kiss for the “Goose Girl”

Nobel Price winner Prof. Otto Hahn visitingPHYWE in 1966


4

PHYSICS – CHEMISTRY – BIOLOGY

The comprehensive catalogue for physics, chemistry

and biology. Additionally you can find a large number of

laboratory materials and an insight in our particularly

successful teaching systems TESS, Cobra3 and

Natural Sciences on the board.

Available in English and Spanish.

Laboratory Experiments

The experiments in the Phywe publication series “Laboratory Experiments”

are intended for the heads of laboratories,

colleges of advanced technology, technical

colleges and similar institutions and also

for advanced courses in high schools.

Laboratory Experiments Physics is

also available on CD-ROM.

Available in English.

For the student system “Advanced Optics

and Laser Physics” a special brochure

is available in English.

Special brochures

Additionally there are special brochu-

res for our particularly successful

teaching systems TESS (available in

German, English, French and Spanish),

Cobra3 (available in German, English)

and Natural Sciences on the board

(available in German, English).

– catalogues, brochures and more…


5PHYWE Systeme GmbH & Co. KG · D-37070 Göttingen Laboratory Experiments Physics

Physics HandbooksPhywe is uncomplicated

To help you in selecting your experiments, we have added pictograms to several of our experiments.

These pictograms give you a quick overview of the most important features of the experiments and provide

you with all the essential information at a glance.

New Products

New products which have been launched in the last few months. Here

you will also find particularly successful experiments with new additional

features to offer you even more measurement and experiment

possibilities.

Our Best-Sellers

Particularly successful and reliable products which have been field-tested

over and over again in numerous countries - some for many years. We

would be more than happy to provide you with references upon request.

Computer-Assisted Experiments with our

Cobra3 PC Interface

A large number of experiments can be performed in a particularly comfor-

table and elegant way with the help of our Cobra3 measurement interfa-

ce. All you need is a PC. The advantage is that you can process the data

particularly well using a PC.

PC interfaced instruments

Some Phywe devices already have an interface included.

These instruments can be connected directly to a PC where you can use

the Phywe measure Software to work with the data.


6 PHYWE Systeme GmbH & Co. KG · D-37070 GöttingenLaboratory Experiments, Physics

Laboratory Experiments, Physics

Picture andEquipment List guarantee time-savingand easy conducting of the experiment.

Theory and evaluation states full theoryinvolved and shows graphical and numericalexperimental results including error calcules.

Example ofmeasurementparameters

All experiments are uniformly built-upand contain references such asRelated topics and Principle and taskto introduce the subject.

LEP5.3.01-11 Hall effect in p-germanium with Cobra3

25301-11PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany

2

Set-up and procedureThe experimental set-up is shown in Fig.1. The test piece on

the board has to be put into the hall-effekt-modul via the guide-

groove. The module is directly connected with the 12V~ output

of the power unit over the ac-input on the backside of the mod-

ule.The connection to the Analog In 2 – port of the Cobra3 Basic-

Unit is realized via a RS232 cable from the RS232-port of the

module.The Tesla-module is connected to the module-port of the

Interface.The plate has to be brought up to the magnet very carefully, so

as not to damage the crystal in particular, avoid bending the

plate. It has to be in the centre between the pole pieces.

The different measurements are controlled by the software.

The magnetic field has to be measured with a hall probe, which

can be directly put into the groove in the module as shown in

Fig.1. So you can be sure that the magnetic flux is measured

directly on the Ge-sample.

To perform the measurements, start the software and choose

as gauge the Cobra3 Hall-Effect.You will receive the following window (Fig.3):

This is the start-screen which appears before every measure-

ment. Here, you can choose, which parameters have to be

measured, displayed, etc., e.g. Hall voltage as a function of

Sample current (Fig.4)

You can also calibrate the Tesla-module via ”options” (Fig.5).

Start the measurement-screen by pressing the ”continue”-but-

ton.

1. Choose The Hall voltage as the measurement-channel and

the Sample current as x-axis.Choose the measurement on ”key press”.Continue. Set the magnetic field to a value of 250 mT by

changing the voltage and current on the power supply.

Determine the hall voltage as a function of the current from

-30 mA up to 30 mA in steps of nearly 5 mA.

You will receive a typical measurement like in Fig.6.

Fig. 3: Start menu of the software Cobra3 Hall effect.

Fig. 4: Example of measurement parameters.

Fig. 5: Calibration menu.

Fig. 2: Hall effect in sample of rectangular section. The polar-

ity sign of the Hall voltage shown applies when the car-

riers are negatively charged.

Fig. 6: Hall voltage as a function of current.

LEP5.3.01

-11Hall effect in p-germanium with Cobra3

25301-11 PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany4

Theory and evaluationIf a current I flows through a conducting strip of rectangularsection and if the strip is traversed by a magnetic field at rightangles to the direction of the current, a voltage – the so-calledHall voltage – is produced between two superposed points onopposite sides of the strip.This phenomenon arises from the Lorentz force: the chargecarriers giving rise to the current flowing through the sampleare deflected in the magnetic field B as a function of their signand their velocity v:

(F = force acting on charge carriers, e = elementary charge).

Since negative and positive charge carriers in semiconductorsmove in opposite directions, they are deflected in the samedirection.

The type of charge carrier causing the flow of current cantherefore be determined from the polarity of the Hall voltage,knowing the direction of the current and that of the magneticfield.

1. Fig. 6 shows that there is a linear relationship between thecurrent I and the Hall voltage UB:

UH = a · I

where a = proportionality factor.2. The change in resistance of the sample due to the magnet-

ic field is associated with a reduction in the mean free pathof the charge carriers. Fig. 7 shows the non-linear, clearlyquadratic, change in resistance as the field strength in-creases. Therefore us the channel modification in theanalysis-menu.

3. In the region of intrinsic conductivity, we have

where s = conductivity, Eg = energy of bandgap, k = Boltz-mann constant, T = absolute temperature.If the logarithm of the conductivity is plotted against T-1 astraight line is obtained with a slope

from which Eg can be determined.

From the measured values used in Fig. 8, the slope of theregression line

is

with a standard deviation sb = ± 0.07 · 103 K.

3. To receive the necessary graph, do as follows:Choose the channel modification in the analysis-menu. Setthe parameters as shown in Fig.11. Continue. Rememberthe procedure with the parameters in Fig.12. Now, you havethe desired graph. To determine the regression line, choosethe ”Regression”-icon.(Since the measurements were made with a constant cur-rent, we can put s ~ U–1, where U is the voltage across thesample.)

Since

we getEg = b · 2k = (0.72 ± 0.03) eV.

k � 8.625 · 10�5 eVK

b � �Eg

2 k � � 4.18 · 103 K

ln s � ln s0 �Eg

2 k · T�1

b � �Eg

2 k .

s � s0 · exp a �Eg

2 kTb

F �

� e 1v � � B 2

Fig. 11: Parameters for the first channel modification.

Fig. 12: Parameters for the second channel modification.

LEP5.3.01

-11Hall effect in p-germanium with Cobra3

PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany 25301-11 1

Related topics

Semiconductor, band theory, forbidden zone, intrinsic conduc-

tivity, extrinsic conductivity, valence band, conduction band,

Lorentz force, magnetic resistance, mobility, conductivity, band

spacing, Hall coefficient.

PrincipleThe resistivity and Hall voltage of a rectangular germanium

sample are measured as a function of temperature and mag-

netic field. The band spacing, the specific conductivity, the type

of charge carrier and the mobility of the charge carriers are

determined from the measurements.

Equipment

Hall effect module,11801.00 1

Hall effect, p-Ge, carrier board 11805.01 1

Coil, 600 turns06514.01 2

Iron core, U-shaped, laminated 06501.00 1

Pole pieces, plane, 30330348mm, 2 06489.00 1

Hall probe, tangent., prot. cap 13610.02 1

Power supply 0-12 V DC/6 V, 12 V AC 13505.93 1

Tripod base -PASS- 02002.55 1

Support rod -PASS-, square, l = 250 mm 02025.55 1

Right angle clamp -PASS- 02040.55 1

Connecting cord, 100 mm, red 07359.01 1

Connecting cord, 100 mm, blue 07359.04 1

Connecting cord, 500 mm, red 07361.01 2

Connecting cord, 500 mm, blue 07361.04 1

Connecting cord, 500 mm, black 07361.05 2

Cobra3 BASIC-UNIT12150.00 1

Cobra3 power supply unit12151.99 1

Tesla measuring module12109.00 1

Cobra3 Software Hall14521.61 1

RS 232 data cable14602.00 2

Tasks1. The Hall voltage is measured at room temperature and con-

stant magnetic field as a function of the control current and

plotted on a graph (measurement without compensation for

defect voltage).

2. The voltage across the sample is measured at room tem-

perature and constant control current as a function of the

magnetic induction B.

3. The voltage across the sample is measured at constant

control current as a function of the temperature. The band

spacing of germanium is calculated from the measure-

ments.

4. The Hall voltage UH is measured as a function of the mag-

netic induction B, at room temperature. The sign of the

charge carriers and the Hall constant RH together with the

Hall mobility mH and the carrier concentration p are calcu-

lated from the measurements.

5. The Hall voltage UH is measured as a function of tempera-

ture at constant magnetic induction B and the values are

plotted on a graph.

Fig.1: Experimental set-up

LABORATORY EXPERIMENTS

PHYSICS

1650

2.12


Klaus Hermbecker

Ludolf von Alvensleben

Regina Butt

Andreas Grünemaier

Robin Sandvoß

Experimental literature

Laboratory Experiments Physics

Print Version No. 16502.32

CD No. 16502.42

The experiments in the PHYWE Publication Series “Laboratory Experiments Physics” are intended for the

heads of physics laboratory courses at universities, colleges of advanced technology, technical colleges and

similar institutions and also for advanced courses in high schools.



Laboratory Experiments, Physics

The present volume which has been developed by PHYWE, complements the previously existing collection

of about 236 experiments in twenty-six chapters as the following comprehensive Table of Contents shows.

In this brochure we present the experiments in short form. The experiments can be ordered or offered

completely or partially, if desired, in accordance with the Comprehensive Equipment Lists. On request, we

will gladly send you detailed experimental descriptions.

You can order the experiments as follows:

� Didactically adap-ted descriptions ofexperiments – easy,direct preparationby the students ispossible

� Comprehensive experiments – cover the entire range of classicaland modern physics

� Developed and proven bypracticians – unproblematical andreliable performance

� Complete equipment offeringmodular experimental set-up –multiple use of individual devices,cost effective and flexible

� Excellent measurement accuracy – results agree with theory

� Computer-assisted experiments –simple, rapid assessement of theresults

Quantity

Order No.

Please specify thisOrder No. if you wouldlike to order the completeexperiment.

Hall effect module, 11801.00 1


Coil, 600 turns 06514.01 2


Pole pieces, plane 06489.00 1

Hall probe, tangent., prot. cap 13610.02 1





Connecting cord, l = 100 mm, red 07359.01 1

Connecting cord, l = 100 mm, blue 07359.04 1

Connecting cord, l = 500 mm, red 07361.01 2

Connecting cord, l = 500 mm, blue 07361.04 1

Connecting cord, l = 500 mm, black 07361.05 2

Cobra3 BASIC-UNIT, USB 12150.50 1

Power supply, 12 V 12151.99 1

Tesla measuring module 12109.00 1

Cobra3 Software Hall 14521.61 1

RS 232 data cable 14602.00 2

PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in p-germanium with Cobra3 P2530111

You can order the experiments as follows:


8 PHYWE Systeme GmbH & Co. KG · D-37070 GöttingenLaboratory Experiments Physics

Summary

1.4.04-00 Viscosity measurements with the falling ball viscometer

1.4.05-00 Surface tension by the ring method (Du Nouy method)

1.4-06-11 Surface tension by the pull-out method with Cobra3

1.4.07-00 Barometric height formula

1.4.08-00 Lift and drag (resistance to flow)

1.5 Mechanical Vibration, Acoustics1.5.01-00 Vibration of strings

1.5.03-11 Velocity of sound in air with Cobra3

1.5.04-01/11 Acoustic Doppler effect

1.5.05-15 Chladni figures with FG-Module

1.5.06-01/15 Velocity of sound using Kundt’s tube

1.5.07-01/15 Wavelengths and frequencies with a Quincke tube

1.5.08-11 Resonance frequencies of Helmholtz resonators with Cobra3

1.5.09-11 Interference of acoustic waves, stationary waves and diffraction at a slot with Cobra3

1.5.10-00 Optical determination of velocity of sound in liquids

1.5.11-00 Phase and group velocity of ultrasonics in liquids

1.5.12-00 Temperature dependence of the Velocity of sound in liquids

1.5.13-00 Stationary ultrasonic waves, determination of wavelength

1.5.14-00 Absorption of ultrasonic in air

1.5.15-15 Ultrasonic diffraction at different single and double slit systems

1.5.16-15 Ultrasonic diffraction at different multiple slit systems

1.5.17-15 Diffraction of ultrasonic waves at a pin hole and a circular obstacle

1.5.18-00 Diffraction of ultrasound at a Fresnel zone plate / Fresnel’s zone construction

1.5.19-15 Interference of two identical ultrasonic transmitters

1.5.20-00 Interference of ultrasonic waves by a Lloyd mirror

1.5.21-11 Determination of the velocity of sound (sonar principle)

1.5.22-00 Ultrasonic Michelson-Interferometer

1.5.23-00 Ultrasonic diffraction by a straight edge

1.5.24-15 Ultrasonic Doppler effect

1.6 Handbooks

Physics Experiments – Linear Motion

Physics Demonstration Experiments –Magnet Board Mechanics 1

Magnet Board Mechanics 2

Optics2.1 Geometrical Optics

2.1.01-00 Measuring the velocity of light

2.1.02-00 Laws of lenses and optical instruments

2.1.03-00 Dispersion and resolving power of the prism and grating spectroscope

2.2 Interference

2.2.01-00 Interference of light

2.2.02-00 Newton’s rings

2.2.03-00 Interference at a mica plate according to Pohl

2.2.04-00 Fresnel’s zone construction / zone plate

2.2.05-00 Michelson interferometer

2.2.06-00 Coherence and width of spectral lines with Michelsoninterferometer

2.2.07-00 Refraction index of air and CO2 with Michelson interferometer

Mechanics1.1 Measurement Techniques

1.1.01-00 Measurement of basic constants: length, weight and time

1.2 Statics1.2.01-00 Moments

1.2.02-00 Modulus of elasticity

1.2.03-00 Mechanical hysteresis

1.3 Dynamics1.3.01-01 Hooke’s law

1.3.01-11 Hooke’s law with Cobra3

1.3.03-01/05 Newton’s second law / Air track or Demonstration track

1.3.03-11/15 Newton’s second law with Cobra3 / Air track or Demonstration track

1.3.05-01/05 Laws of collision / Air track or Demonstration track

1.3.05-11/15 Laws of collision with Cobra3 / Air track or Demonstration track

1.3.07-01 Free fall

1.3.07-11 Free fall with Cobra3

1.3.09-01 Determination of the gravitational constant with a Cavendish balance

1.3.11-00 Projectile motion

1.3.12-00 Ballistic Pendulum

1.3.13-01 Moment of inertia and angular acceleration

1.3.13-11 Moment of inertia and angular acceleration with Cobra3

1.3.15-00 Moment and angular momentum

1.3.16-01 Centrifugal force

1.3.16-11 Centrifugal force with Cobra3

1.3.18-00 Mechanical conservation of energy / Maxwell’s wheel

1.3.19-00 Laws of gyroscopes / 3-axis gyroscope

1.3.20-00 Laws of gyroscopes / cardanic gyroscope

1.3.21-00 Mathematical pendulum

1.3.22-00 Reversible pendulum

1.3.23-01 Pendulum oscillations / variable g pendulum

1.3.23-11 Pendulum oscillations with Cobra3

1.3.25-01 Coupled Pendula

1.3.25-11 Coupled Pendula with Cobra3

1.3.26-11 Harmonic oscillations of spiral springs – Springs linked in parallel and series

1.3.27-01 Forced Oscillations – Pohl’s pendulum

1.3.27-11 Forced Oscillations – Pohl’s pendulum; Determination of resonance frequencies by Fourier analysis

1.3.28-01 Moments of inertia / Steiner’s theorem

1.3.28-11 Moments of inertia of different bodies / Steiner’s theorem with Cobra3

1.3.30-00 Torsional vibrations and torsion modulus

1.3.31-00 Moment of inertia and torsional vibrations

1.3.32-00 The propagation of a periodically excited continuous transverse wave

1.3.33-00 Phase velocity of rope waves

1.3.34-00 Wave phenomena in a ripple tank

1.3.35-00 Interference and diffraction of water waves with the ripple tank

1.4 Mechanics of Liquids and Gaseous Bodies1.4.01-00 Density of liquids

1.4.02-00 Surface of rotating liquids

1.4.03-00 Viscosity of Newtonian and non-Newtonian liquids (rotary viscometer)

1

2



Summary

3

4

2.3 Diffraction

2.3.01-00 Diffraction at a slit and Heisenberg’s uncertainty principle

2.3.02-00 Diffraction of light at a slit and an edge

2.3.03-00 Intensity of diffractions due to pin hole diaphragms and circular obstacles

2.3.04-00 Diffraction intensity for multiple slits and grids

2.3.05-00 Determination of the diffraction intensity at slit and double slit systems

2.3.06-00 Diffraction intensity through a slit and a wire – Babinet’s theorem

2.4 Photometry

2.4.02-01 Photometric law of distance

2.4.02-11 Photometric law of distance with Cobra3

2.4.04-00 Lambert’s law

2.5 Polarisation2.5.01-00 Polarisation by quarterwave plates

2.5.02-00 Polarimetry

2.5.03-00 Fresnel’s equations – theory of reflection

2.5.04-00 Malus’ law

2.6 Applied Optics

2.6.01-00 Faraday effect

2.6.02-00 Kerr effect

2.6.03-00 Recording and reconstruction of holograms

2.6.04-00 CO2-laser

2.6.05-11 LDA – Laser Doppler Anemometry with Cobra3

2.6.07-01 Helium Neon Laser

2.6.08-00 Optical pumping

2.6.09-00 Nd-YAG laser

2.6.10-00 Fibre optics

2.6.11-00 Fourier optics – 2f Arrangement

2.6.12-00 Fourier optics – 4f Arrangement – Filtering and reconstruction

2.7 Handbooks

Advanced Optics and Laser Physics – Handbook 1–3

Physics Demonstration Experiments – Magnet Board Optics

Thermodynamics3.1 Thermal Expansion

3.1.01-00 Thermal expansion in solids and liquids

3.2 Ideal and Real Gases

3.2.01-01 Equation of state of ideal gases

3.2.01-15 Equation of state of ideal gases with Cobra3

3.2.02-01 Heat capacity of gases

3.2.02-11 Heat capacity of gases with Cobra3

3.2.03-00 Maxwellian velocity distribution

3.2.04-00 Thermal equation of state and critical point

3.2.05-00 Adiabatic coefficient of gases – Flammersfeld oscillator

3.2.06-00 Joule-Thomson effect

3.3 Calorimetry, Friction Heat

3.3.01-01 Heat capacity of metals

3.3.01-11 Heat capacity of metals with Cobra3

3.3.02-00 Mechanical equivalent of heat

3.4 Phase Transitions

3.4.01-00 Vapour pressure of water at high temperature

3.4.02-00 Vapour pressure of water below 100°C /Molar heat of vaporization

3.4.03-00 Boiling point elevation

3.4.04-00 Freezing point depression

3.5 Transport and Diffusion

3.5.01-01/15 Stefan-Boltzmann’s law of radiation

3.5.02-00 Thermal and electrical conductivity of metals

3.6 Applied Thermodynamics

3.6.01-00 Solar ray Collector

3.6.02-00 Heat pump

3.6.03-00 Heat insulation / Heat conduction

3.6.04-01/15 Stirling engine

3.7 Handbooks

Glas jacket system

Demonstration Experiments Physics – Magnetic Board Heat

Electricity4.1 Stationary Currents

4.1.01-01 Measurement of small resistance

4.1.01-15 Ohm’s Law with FG-Module

4.1.02-00 Wheatstone Bridge

4.1.03-00 Internal resistance and matching in voltage source

4.1.04-01/15 Temperature dependence of different resistors and diodes

4.1.06-01/15 Current balance/Force acting on a current-carrying conductor

4.1.07-00 Semiconductor thermogenerator

4.1.08-00 Peltier heat pump

4.1.09-01 Characteristic curves of a solar cell

4.1.09-15 Characteristic curves of semiconductors with FG-Module

4.1.11-00 Characteristic and efficiency of PEM fuel cell and PEM electrolyser

4.1.12-00 Faraday’s law

4.1.13-15 Second order conductors. Electrolysis with FG-Module

4.2 Electric Field

4.2.01-00 Electrical fields and potentials in the plate capacitor

4.2.02-00 Charging curve of a capacitor

4.2.02-15 Switch-on behaviour of a capacitor and an inductivity with FG-Module

4.2.03-00 Capacitance of metal spheres and of a spherical capacitor

4.2.04-01 Coulomb’s law / Image charge

4.2.04-15 Coulomb’s law with Cobra3

4.2.05-00 Coulomb potential and Coulomb field of metal spheres

4.2.06-00 Dielectric constant of different materials

4.3 Magnetic Field

4.3.01-00 Earth’s magnetic field

4.3.02-01/15 Magnetic field of single coils / Biot-Savart’s law

4.3.03-01/15 Magnetic field of paired coils in Helmholtz arrangement

4.3.04-00 Magnetic moment in the magnetic field



Summary

4.3.05-00 Magnetic field outside a straight conductor

4.3.06-00 Magnetic field inside a conductor

4.3.07-11 Ferromagnetic hysteresis

4.3.08-00 Magnetostriction with the Michelson interferometer

4.4 Electrodynamics4.4.01-00 Transformer

4.4.02-01/15 Magnetic induction

4.4.03-01/11 Inductance of solenoids

4.4.04-01/11 Coil in the AC circuit with Cobra3

4.4.05-01/15 Capacitor in the AC circuit

4.4.06-01/11 RLC Circuit with Cobra3

4.4.07-00 Rectifier circuits

4.4.08-00 RC Filters

4.4.09-01/15 High-pass and low-pass filters

4.4.10-00 RLC measuring bridge

4.4.11-00 Resistance, phase shift and power in AC circuits

4.4.12-11 Induction impulse

4.5 Electromagnetic Oscillations and Waves4.5.02-00 Coupled oscillating circuits

4.5.04-00 Interference of microwaves

4.5.05-00 Diffraction of microwaves

4.5.06-00 Diffraction and polarization of microwaves

4.5.08-00 Radiation field of a horn antenna / Microwaves

4.5.09-00 Frustrated total reflection / Microwaves

4.6 HandbooksDemonstration Experiments Physics – Electricity/Electronics on the Magnetic Board 1 + 2

Physical Structure of Matter5.1 Physics of the Electron5.1.01-00 Elementary charge and Millikan experiment

5.1.02-00 Specific charge of the electron – e/m

5.1.03-11 Franck-Hertz experiment with Hg-tube

5.1.03-15 Franck-Hertz experiment with Ne-tube

5.1.04-01/05 Planck’s “quantum of action” from photoelectric effect (line separation by interference filters)

5.1.05-01/05 Planck’s “quantum of action” from the photoelectric effect (line separation by defraction grating)

5.1.06-00 Fine structure, one-electron and two-electron spectra

5.1.07-00 Balmer series / Determination of Rydberg’s constant

5.1.08-00 Atomic spectra of two-electron systems: He, Hg

5.1.10-05 Zeeman effect

5.1.11-01/11 Stern-Gerlach experiment

5.1.12-00 Electron spin resonance

5.1.13-00 Electron diffraction

5.2 Radioactivity5.2.01-01 Half-life and radioactive equilibrium

5.2.01-11 Half-life and radioactive equilibrium with Cobra3

5.2.03-11 Poisson’s distribution and Gaussian distribution of radioactive decay with Cobra3 – Influence of the dead time of the counter tube

5.2.04-00 Visualisation of radioactive particles / Diffusion cloud chamber

5.2.20-15 Alpha-Energies of different sources with MCA

5.2.21-01/11/15 Rutherford experiment

5.2.22-01/11/15 Fine structure of the �-spectrum of 241Am

5.2.23-01/11/15 Study of the �-energies of 226Ra

5.2.24-01/11/15 Energy loss of �-particles in gases

5.2.31-00 Electron absorption

5.2.32-00 �-spectroscopy

5.2.41-01/11 Law of distance and absorption of gamma or beta rays

5.2.42-01/11/15 Energy dependence of the �-absorption coefficient

5.2.44-01/11/15 Compton effect

5.4.45-01/11/15 Internal conversion in 137mBa

5.2.46-01/11/15 Photonuclear cross-section / Compton scattering cross-section

5.2.47-01/11/15 X-ray fluorescence and Moseley’s law

5.3 Solid-state Physics, Plasma Physics5.3.01-01 Hall effect in p-germanium

5.3.01-11 Hall effect in p-germanium with Cobra3

5.3.02-01/11 Hall effect in n-germanium

5.3.03-00 Hall effect in metals

5.3.04-01 Band gap of germanium

5.3.04-11 Band gap of germanium with Cobra3

5.3.10-00 Surface treatment / Plasma Physics

5.3.11-00 Paschen curve / Plasma Physics

5.4 X-ray Physics5.4.01-00 Characteristic X-rays of copper5.4.02-00 Characteristic X-rays of molybdenum5.4.03-00 Characteristic X-rays of iron5.4.04-00 The intensity of characteristic X-rays as a function of anode

current and anode voltage5.4.05-00 Monochromatization of molybdenum X-rays5.4.06-00 Monochromatization of copper X-rays5.4.07-00 K� doublet splitting of molybdenum X-rays / fine structure5.4.08-00 K� doublet splitting of iron X-rays / fine structure5.4.09-00 Duane-Hunt displacement law and Planck's “quantum of action”5.4.10-00 Characteristic X-ray lines of different anode materials /

Moseley's Law; Rydberg frequency and screening constant5.4.11-00 Absorption of X-rays5.4.12-00 K- and L-absorption edges of X-rays /

Moseley's Law and the Rydberg constant5.4.13-00 Examination of the structure of NaCl monocrystals with

different orientations5.4.14/15-00 X-ray investigation of different crystal structures /

Debye-Scherrer powder method5.4.16-00 X-ray investigation of crystal structures / Laue method5.4.17-00 Compton scattering of X-rays5.4.18-00 X-ray dosimetry5.4.19-00 Contrast medium experiment with a blood vessel model5.4.20-00 Determination of the length and position of an object

which cannot be seen5.4.21-00 Diffractometric Debye-Scherrer patterns of powder samples

with the three cubic Bravais lattices5.4.22-00 Diffractometric Debye-Scherrer patterns of powder samples

with diamond structure (germanium and silicon)5.4.23-00 Diffractometric Debye-Scherrer patterns of powder samples

with a hexagonal lattice structure5.4.24-00 Diffractometric Debye-Scherrer patterns of powder samples

with a tetragonal lattice structure5.4.25-00 Diffractometric Debye-Scherrer patterns of powder samples

with a cubic powder sample5.4.26-00 Diffractometric measurements to determine the intensity of

Debye-Scherrer reflexes using a cubic lattice powder sample5.4.27-00 Diffractometric Debye-Scherrer measurements

for the examination of the texture of rolled sheets5.4.28-00 Characteristic X-rays of tungsten 5.4.40-00 Spectroscopy with the X-ray energy detector

5.4 Handbooks

X-Ray Experiments

Interface-System Cobra3 Physics and Chemistry/Biology

5


1Mechanics

LEP_1_1 09.08.2007 11:15 Uhr Seite 11


Contents

1.1 Measurement Techniques1.1.01-00 Measurement of basic constants: length, weight and time

1.2 Statics1.2.01-00 Moments1.2.02-00 Modulus of elasticity1.2.03-00 Mechanical hysteresis

1.3 Dynamics1.3.01-01 Hooke’s law1.3.01-11 Hooke’s law with Cobra31.3.03-01/05 Newton’s second law / Air track or Demonstration track1.3.03-11/15 Newton’s second law with Cobra3 / Air track or

Demonstration track1.3.05-01/05 Laws of collision / Air track or Demonstration track1.3.05-11/15 Laws of collision with Cobra3 / Air track or Demonstration track1.3.07-01 Free fall1.3.07-11 Free fall with Cobra31.3.09-01 Determination of the gravitational constant

with a Cavendish balance1.3.11-00 Projectile motion1.3.12-00 Ballistic Pendulum1.3.13-01/05 Moment of inertia and angular acceleration1.3.13-11/15 Moment of inertia and angular acceleration with Cobra31.3.15-00 Moment and angular momentum1.3.16-01 Centrifugal force1.3.16-11 Centrifugal force with Cobra31.3.18-00 Mechanical conservation of energy / Maxwell’s wheel1.3.19-00 Laws of gyroscopes / 3-axis gyroscope1.3.20-00 Laws of gyroscopes / cardanic gyroscope1.3.21-00 Mathematical pendulum1.3.22-00 Reversible pendulum1.3.23-01 Pendulum oscillations / variable g pendulum1.3.23-11 Pendulum oscillations with Cobra31.3.25-01 Coupled Pendula1.3.25-11 Coupled Pendula with Cobra31.3.26-11 Harmonic oscillations of spiral springs –

Springs linked in parallel and series1.3.27-01 Forced Oscillations – Pohl’s pendulum1.3.27-11 Forced Oscillations – Pohl’s pendulum;

Determination of resonance frequencies by Fourier analysis1.3.28-01 Moment of inertia / Steiner’s theorem1.3.28-11 Moments of inertia of different bodies /

Steiner’s theorem with Cobra31.3.30-00 Torsional vibrations and torsion modulus


1.3.32-00 The propagation of a periodically excited continuous transverse wave

Mechanics


1.3.34-00 Wave phenomena in a ripple tank


1.4 Mechanics of Liquids and Gaseous Bodies1.4.01-00 Density of liquids1.4.02-00 Surface of rotating liquids1.4.03-00 Viscosity of Newtonian and non-Newtonian liquids

(rotary viscometer)1.4.04-00 Viscosity measurements with the falling ball viscometer1.4.05-00 Surface tension by the ring method (Du Nouy method)1.4-06-11 Surface tension by the pull-out method with Cobra31.4.07-00 Barometric height formula1.4.08-00 Lift and drag (resistance to flow)

1.5 Mechanical Vibration, Acoustics1.5.01-00 Vibration of strings1.5.03-11 Velocity of sound in air with Cobra31.5.04-01/11 Acoustic Doppler effect1.5.05-15 Chladni figures with FG-Module1.5.06-01/15 Velocity of sound using Kundt’s tube1.5.07-01/15 Wavelengths and frequencies with a Quincke tube1.5.08-11 Resonance frequencies of Helmholtz resonators with Cobra31.5.09-11 Interference of acoustic waves, stationary waves and diffraction

at a slot with PC interface1.5.10-00 Optical determination of velocity of sound in liquids1.5.11-00 Phase and group velocity of ultrasonics in liquids1.5.12-00 Temperature dependence of the Velocity of sound in liquids1.5.13-00 Stationary ultrasonic waves, determination of wavelength1.5.14-00 Absorption of ultrasonic in air1.5.15-15 Ultrasonic diffraction at different single and double slit systems 1.5.16-15 Ultrasonic diffraction at different multiple slit systems1.5.17-15 Diffraction of ultrasonic waves at a pin hole and a circular obstacle1.5.18-00 Diffraction of ultrasound at a Fresnel zone plate /

Fresnel’s zone construction1.5.19-15 Interference of two identical ultrasonic transmitters1.5.20-00 Interference of ultrasonic waves by a Lloyd mirror1.5.21-15 Determination of the velocity of sound (sonar principle)1.5.22-00 Ultrasonic Michelson-Interferometer1.5.23-00 Ultrasonic diffraction by a straight edge1.5.24-15 Ultrasonic Doppler effect

1.6 Handbooks

Physics Experiments – Linear MotionPhysics Demonstration Experiments – Magnet Board Mechanics 1Physics Demonstration Experiments – Magnet Board Mechanics 2

1LEP_1_1 09.08.2007 11:15 Uhr Seite 12


Measurement of basic constants: length, weight and time 1.1.01-00

Measurement Techniques Mechanics

Principle:Caliper gauges, micrometers andspherometers are used for the accu-rate measurement of lengths, thick-nesses, diameters and curvatures. Amechanical balance is used forweight determinations, a decadecounter is used for accurate timemeasurements. Measuring proce-dures, accuracy of measurement andreading accuracy are demonstrated.

Vernier caliper

Tasks:1. Determination of the volume of

tubes with the caliper gauge.

2. Determination of the thickness ofwires, cubes and plates with themicrometer.

3. Determination of the thickness ofplates and the radius of curvatureof watch glasses with the sphe-rometer.

What you can learn about …

� Length� Diameter� Inside diameter thickness� Curvature� Vernier� Weight resolution� Time measurement

Vernier calipers, stainless steel 03010.00 1Micrometer 03012.00 1Spherometer 03017.00 1Light barrier, compact 11207.20 1Digital counter, 4 decades 13600.93 1Alternatively to 13600.93:Timer 2-1 13607.99 1

Precision balance, double pan type, 500 g 44011.50 1Set of precision weights, 1 mg...200 g, in case 44070.20 1Iron column 03913.00 1Iron wire, d = 1.0 mm, l = 10 m 06104.01 1Aluminium foil, 4 sheets 06270.00 1Glass plate, 100 mm x 85 mm x 1 mm 08203.00 1Watch glass, d = 80 mm 34572.00 1Watch glass, d = 100 mm 34574.00 1Watch glass, d = 125 mm 34575.00 1Glass tube, AR-glass, straight, d = 8 mm, l = 80 mm, 10 pcs. 36701.65 1Glass tubes, AR-glass, d = 24 mm, l = 120 mm 45158.00 1Cubes, set of 8 02214.00 1Fishing line on spool, d = 0,5 mm, l = 100 mm 02090.00 1Steel balls with eyelet, d = 32 mm 02466.01 1Rod with hook 02051.00 1Support rod -PASS-, square, l = 630 mm 02027.55 1Tripod base -PASS- 02002.55 1Right angle clamp -PASS- 02040.55 2Measuring tape, l = 2 m 09936.00 1Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 1Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 1Connecting cable, 4 mm plug, 32 A, yellow, l = 50 cm 07361.02 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMeasurement of basic constants: length, weight and time P2110100

Knife-edge measuring facesfor inside measurement

Slide Guide barDepth measuring

Measuring facesfor depthmeasurement

Graduated scaleVernier

Movable jaw blade

Measuring facesfor outsidemeasurement

Fixedjawblade

LEP_1_1 09.08.2007 11:15 Uhr Seite 13


1.2.01-00 Moments

Principle:Coplanar forces (weight, spring bal-ance) act on the moments disc oneither side of the pivot. In equilibri-um, the moments are determined asa function of the magnitude anddirection of the forces and of thereference point.

Moment as a function of the distance between the origin of the coordinatesand the point of action of the force.

Tasks:1. Moment as a function of the dis-

tance between the origin of thecoordinates and the point of ac-tion of the force,

2. moment as a function of the anglebetween the force and the posi-tion vector to the point of actionof the force,

3. moment as a function of the force.

Moments disk 02270.00 1

Precision spring balance 1 N 03060.01 2


Barrel base -PASS- 02006.55 1



Swivel clamp -PASS- 02041.55 1

Bolt with pin 02052.00 1

Weight holder for slotted weights 02204.00 1

Slotted weights, 10 g, coated black 02205.01 4

Slotted weight, 50 g, coated black 02206.01 1

Fishing line on spool, d = 0,5 mm, l = 100 mm 02090.00 1

Rule, plastic, 200 mm 09937.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMoments P2120100

Mechanics Statics


� Moments� Couple� Equilibrium� Statics� Lever� Coplanar forces

m = 0.1 kg

r2 = 0.12 m

� = �/2.

LEP_1_1 09.08.2007 11:15 Uhr Seite 14


Modulus of elasticity 1.2.02-00

Statics Mechanics

Principle:A flat bar is supported at two points.It is bent by the action of a forceacting at its centre. The modulus ofelasticity is determined from thebending and the geometric data ofthe bar.

Table 1: The modulus of elasticity for different materials.

Tasks:1. Determination of the characteris-

tic curve of the dial gauge

2. Determination the bending of flatbars as a function

● of the force

● of the thickness, at constantforce

● of the width, at constant force

● of the distance between thesupport points at constant force

3. Determination the modulus ofelasticity of steel, aluminium andbrass.


� Young’s modulus� Modulus of elasticity� Stress� Deformation� Poisson’s ratio� Hooke’s law

Dial gauge, 10/0.01 mm 03013.00 1

Holder for dial gauge 03013.01 1

Flat rods, set 17570.00 1

Knife-edge with stirrup 03015.00 1

Bolt with knife edge 02049.00 2









Measuring tape, l = 2 m 09936.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedModulus of elasticity P2120200

Material Dimensions [mm] E �N · m-2�

Steel 10�1.5 2.059 · 1011

Steel 10�2 2.063 · 1011

Steel 10�3 2.171· 1011

Steel 15�1.5 2.204 · 1011

Steel 20�1.5 2.111 · 1011

Aluminium 10�2 6.702 · 1010

Brass 10�2 9.222 · 1010

LEP_1_1 09.08.2007 11:15 Uhr Seite 15


1.2.03-00 Mechanical hysteresis

Principle:The relationship between torque andangle of rotation is determined whenmetal bars are twisted. The hystere-sis curve is recorded.

Mechanical hysteresis curve for the torsion of a copper rod of 2 mm diameterand 0.5 m long.

Tasks:1. Record the hysteresis curve of

steel and copper rods.

2. Record the stress-relaxation curvewith various relaxation times ofdifferent materials.

Torsion apparatus 02421.00 1

Torsion rod, steel, d = 2 mm, l = 500 mm 02421.01 1

Torsion rod, Al, d = 2 mm, l = 500 mm 02421.02 1





Torsion rod, brass, d = 2 mm, l = 500 mm 02421.07 1

Torsion rod, copper, d = 2 mm, l = 500 mm 02421.08 1


Precision spring balances, 2.5 N 03060.02 1

Stopwatch, digital, 1/100 s 03071.01 1

Support base -PASS- 02005.55 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedMechanical hysteresis P2120300

Mechanics Statics


� Mechanical hysteresis� Elasticity� Plasticity� Relaxation� Torsion molulus� Plastic flow� Torque� Hooke’s law

LEP_1_1 09.08.2007 11:15 Uhr Seite 16


Hooke’s law 1.3.01-01

Statics Mechanics

2,0

1,5

1,0

0,5

0

X

0 2 4 6 8 � lcm

FwN

10 12 14 16 18

XX

XX

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

B

A

Principle:The validity of Hooke's law is deter-mined for two helical springs withdifferent spring constants. The elon-gation of the helical spring, whichdepends on the deforming force, isstudied by means of the weights ofmasses. For comparison, a rubberband, for which no proportionalityexists between the exerted force andthe resulting elongation, is submit-ted to the same forces.

Acting weight Fw as a function of the extension �l for a rubber band (elastic hysteresis).

Tasks:1. Determining the spring constants

of helical springs

2. Study of the elongation of a rub-ber band


� Hooke's law� Spring constant� Limit of elasticity� Elastic hysteresis� Elastic after-effect





Cursor for scale, 2 pieces, plastic, red 02201.00 1



Slotted weights, 10 g, silver colour 02205.02 2


Slotted weights, 50 g, silver bronzing 02206.02 2

Helical springs, 3 N/m 02220.00 1


Silk thread on spool, l = 200 mm 02412.00 1

Meter Scale, l = 1000 x 27 mm 03001.00 1

Holding pin 03949.00 1

Square section rubber strip, l = 10 m 03989.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedHooke’s law P2130101

Theory (Hook’s Law)

Experiment

LEP_1_1 09.08.2007 11:15 Uhr Seite 17


1.3.01-11 Hooke’s law with Cobra3

Principle:The validity of Hooke’s Law is provenusing various helical springs withdifferent spring constants. In com-parison, the behaviour of a stretchedrubber band is examined, for whichthere is no proportionality betweenacting force and resulting extension.

Characteristic elongation curve for a helical spring with D = 20 N/m.

Tasks:1. Calibration of the system (move-

ment sensor and force sensor).

2. Measurement of the tensile forceas a function of the path for threedifferent helical springs and a rub-ber band.

3. Determination of the spring con-stant and evaluation of a hystere-sis curve.

4. Verification of Hooke’s law.

Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 1Software Cobra3 Force/Tesla 14515.61 1Square section rubber strip, l = 10 m 03989.00 1Newton measuring module 12110.00 1Newton Sensor 12110.01 1Movement sensor with cable 12004.10 1Adapter BNC socket/4 mm plug pair 07542.27 1Adapter, BNC socket - 4 mm plug 07542.20 1Helical springs, 3 N/m 02220.00 1Helical springs, 20 N/m 02222.00 1Helical springs, 30 N/m 02224.00 1Right angle clamp -PASS- 02040.55 2Support rod -PASS-, square, l = 1000 mm 02028.55 1Stand tube 02060.00 1Barrel base -PASS- 02006.55 1Bench clamp -PASS- 02010.00 1Plate holder, opening width 0...10 mm 02062.00 1Meter Scale, l = 1000 x 27 mm 03001.00 1Nylon thread on spool, d = 0,4 mm, l = 50 mm 02095.00 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedHooke’s law with Cobra3 P2130111

Mechanics Statics


� Spring constant� Limit of elasticity� Extension and compression

LEP_1_1 09.08.2007 11:15 Uhr Seite 18


Newton’s second law / Air track or Demonstration track 1.3.03-01/05

Principle:The distance-time law, the velocity-time law, and the relationship be-tween mass, acceleration and forceare determined with the aid of theair track rail for uniformly accelerat-ed motion in a straight line.

Tasks:Determination of:

1. Distance travelled as a function oftime

2. Velocity as a function of time

3. Acceleration as a function of theaccelerated mass

4. Acceleration as a function offorce.


� Velocity� Acceleration� Force� Acceleration of gravity

Experiment P2130305 with demo trackExperiment P2130301 with air trackTimer 4-4 13605.99 1 1Light barrier, compact 11207.20 4 4Precision pulley 11201.02 1Air track rail 11202.17 1Blower 230V/50Hz 13770.97 1Pressure tube, l = 1.5 m 11205.01 1Glider for air track 11202.02 1Diaphragm, l = 100 mm 11202.03 1Slotted weights, 1 g, polished 03916.00 20 20Slotted weights, 10 g, coated black 02205.01 8 8Slotted weight, 50 g, coated black 02206.01 4 4Stop, adjustable 11202.19 1Endholder for air track rail 11202.15 1Starter system, mechanical with release 11202.13 1Starter system for motion track 11309.00 1Magnet with plug for starter system 11202.14 1 1Fork with plug 11202.08 1 1Tube with plug 11202.05 1 1Plasticine, 10 sticks 03935.03 1 1Hook with plug 11202.07 1 1Silk thread on spool, l = 200 mm 02412.00 1 1Weight holder, 1g, silver bronzing 02407.00 1 1Barrel base -PASS- 02006.55 4Support rod -PASS-, square, l = 400 mm 02026.55 4Right angle clamp -PASS- 02040.55 4Shutter plate for low friction cart, w = 100 mm 11308.00 1Needle with plug 11202.06 1 1Demonstration Track, Aluminium, l = 1.5 m 11305.00 1Cart, low friction sapphire bearings 11306.00 1Pulley for demonstration track 11305.10 1Holder for pulley 11305.11 1Weight for low friction cart, 400 g 11306.10 1End holder for demonstration track 11305.12 1Holder for light barrier 11307.00 4Portable Blance, OHAUS CS2000 48892.00 1 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedNewton’s second law / Air track or Demonstration track P21303 01/05

The distance travelled s plotted as a function of the time t ; m1 = 10 g, m2 = 201 g.

Dynamics Mechanics

Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 4 4Connecting cable, 4 mm plug, 32 A, yellow, l = 100 cm 07363.02 4 4Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 4 4Connecting cable, 4 mm plug, 32 A, yellow, l = 200 cm 07365.02 4 1Connecting cable, 4 mm plug, 32 A, black, l = 200 cm 07365.05 4 1

You can find more

experiments in experimental literature

“Linear Motion”

Order No. 16001.02 (see page 84)

Set-up of experiment P2130301 with air track

LEP_1_1 09.08.2007 11:15 Uhr Seite 19


1.3.03-11/15 Newton’s second law with Cobra3 / Air track or Demonstration track

Principle:According to Newton’s 2nd law ofmotion for a mass point, the rela-tionship between mass, accelerationand force are investigated.

Path-time law.

Tasks:The distance-time law, the velocity-time law and the relationship be-tween mass, acceleration and forceare determined. The conservation ofenergy can be investigated.

Experiment P2130311 with air trackExperiment P2130315 with demo track

Cobra3 BASIC-UNIT, USB 12150.50 1 1

Power supply 12V/2A 12151.99 1 1

Software Cobra3, Translation/ Rotation 14512.61 1 1

Light barrier, compact 11207.20 1 1

Air track rail 11202.17 1

Blower 230V/50Hz 13770.97 1

Pressure tube, l = 1.5 m 11205.01 1

Glider for air track 11202.02 1

Slotted weights, 1 g, polished 03916.00 20 9

Slotted weights, 10 g, coated black 02205.01 4 4

Slotted weights, 50 g, silver bronzing 02206.02 4 4

Stop, adjustable 11202.19 1

Starter system, mechanical with release 11202.13 1

Magnet with plug for starter system 11202.14 1

Tube with plug 11202.05 1 1

Plasticine, 10 sticks 03935.03 1 1

Hook with plug 11202.07 1 1

Silk thread on spool, l = 200 mm 02412.00 1 1

Weight holder, 1 g, silver bronzing 02407.00 1 1

Bench clamp -PASS- 02010.00 1

Bosshead 02043.00 2

Support rod, stainless steel 18/8, l = 250 mm, d = 10 mm 02031.00 1

Support rod, stainless steel 18/8, l = 100 mm 02030.00 1

Measuring tape, l = 2 m 09936.00 1 1

Needle with plug 11202.06 1 1

Demonstration Track, Aluminium, l = 1.5 m 11305.00 1

Cart, low friction sapphire bearings 11306.00 1

Holder for pulley 11305.11 1

Weight for low friction cart, 400 g 11306.10 1

End holder for demonstration track 11305.12 2

Portable Blance, OHAUS CS2000 48892.00 1 1

Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 1 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedNewton’s second law with Cobra3 / Air track or Demonstration track P2130311/15

Mechanics Dynamics


� Linear motion� Velocity� Acceleration� Conservation of energy

Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 1 1

Connecting cable, 4 mm plug, 32 A, yellow, l = 100 cm 07363.02 1 1

Connecting plug, pack of 2 07278.05 1 1

Crocodile clips, black, plastic insulation, pack of 10 07276.15 1 1


Set-up of experiment P2130315 with demo track

LEP_1_1 09.08.2007 11:15 Uhr Seite 20


Dynamics Mechanics

Laws of collision / Air track or Demonstration track 1.3.05-01/05

Principle:The volocities of two gliders, movingwithout friction on an air-cushiontrack, are measured before and aftercollision, for both elastic and inelas-tic collision.

Tasks:1. Elastic collision1.1 The impulses of the two gliders

as well as their sum after thecollision. For comparison themean value of the impulses ofthe first glider is entered as ahorizontal line in the graph.

1.2 Their energies, in a manner anal-ogous to Task 1.1

1.3 In accordance with the meanvalue of the measured impulse ofthe first glider before the colli-sion, the theoretical values of theimpulses for the two gliders areentered for a range of massratios from 0 to 3. For purposesof comparison the measuringpoints (see 1.1) are plotted in thegraph.

1.4 In accordance with the meanvalue of the measured energy ofthe first glider before the colli-

Elastic collision: calculated energies after the collision as functions of themass ratio of the gliders.


� Conservation of momentum� Conservation of energy� Linear motion� Velocity� Elastic loss� Elastic collision

Experiment P2130505 with demo trackExperiment P2130501 with air track

Air track rail 11202.17 1Blower 230V/50Hz 13770.97 1Pressure tube, l = 1.5 m 11205.01 1Glider for air track 11202.02 2Diaphragm, l = 100 mm 11202.03 2Tube with plug 11202.05 2 2Needle with plug 11202.06 1 2Fork with plug 11202.08 1 1Rubber bands for fork with plug, 10 pcs. 11202.09 1 1Plate with plug 11202.10 1 1Starter system, mechanical with release 11202.13 1Magnet with plug for starter system 11202.14 1 1Endholder for air track rail 11202.15 1Slotted weights, 10 g, coated black 02205.01 10 10Slotted weight, 50 g, coated black 02206.01 6 6Light barrier, compact 11207.20 2 2Timer 4-4 13605.99 1 1Portable Blance, OHAUS CS2000 48892.00 1 1Barrel base -PASS- 02006.55 2Support rod -PASS-, square, l = 400 mm 02026.55 2Right angle clamp -PASS- 02040.55 2Demonstration Track, Aluminium, l = 1.5 m 11305.00 1Cart, low friction sapphire bearings 11306.00 2Starter system for motion track 11309.00 1Weight for low friction cart, 400 g 11306.10 2Shutter plate for low friction cart, w = 100 mm 11308.00 2Holder for light barrier 11307.00 2End holder for demonstration track 11305.12 1Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 2 2Connecting cable, 4 mm plug, 32 A, yellow, l = 100 cm 07363.02 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 2 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of collision / Air track or Demonstration track P21305 01/05

sion, the theoretical values of theenergy after the collision areplotted analogously to Task 1.3.In the process, the measured val-ues are compared with the theo-retical curves.

2. Inelastic collision2.1 The impulse values are plotted as

in Task 1.1.

2.2 The energy values are plotted asin Task 1.2.

2.3 The theoretical and measuredimpulse values are compared asin Task 1.3.

2.4 As in Task 1.4, the theoretical anmeasured energy values arecompared. In order to clearlyillustrate the energy loss and itsdependence on the mass ratios,the theoretical functions of thetotal energy of both gliders andthe energy loss after the collisionare plotted.

Set-up of experiment P2130505 with demo track

LEP_1_1 09.08.2007 11:15 Uhr Seite 21


1.3.05-11/15 Laws of collision with Cobra3 / Air track or Demonstration track

Principle:The velocity of two gliders, movingwithout friction on an air-cushiontrack, are measured before and aftercollision, for both elastic and inelas-tic collision.

Tasks:1. Elastic collision

A glider whose mass always re-mains unchanged collides with asecond resting glider at a constantvelocity. A measurement series, inwhich the velocities of the firstglider before the collision and thevelocities of both gliders after itare to be measured, is conductedby varying mass of the restingglider.

Measuring parameters for velocity measurement

2. Inelastic collisionA glider, whose mass always re-mains unchanged, collides with aconstant velocitiy with a secondresting glider. A measurement se-ries with different masses of theresting glider is performed: thevelocities of the first glider beforethe collision and those of bothgliders, which have equal veloci-ties, after it are to be measured.

Experiment P2130515 with demo trackExperiment P2130511 with air trackAir track rail 11202.17 1Blower 230V/50Hz 13770.97 1Pressure tube, l = 1.5 m 11205.01 1Glider for air track 11202.02 1Diaphragm, l = 100 mm 11202.03 2Tube with plug 11202.05 2 2Needle with plug 11202.06 2 2Fork with plug 11202.08 1 1Rubber bands for fork with plug, 10 pcs. 11202.09 1 1Plate with plug 11202.10 1 1Starter system, mechanical with release 11202.13 1Magnet with plug for starter system 11202.14 1 1Endholder for air track rail 11202.15 2Slotted weights, 10 g, coated black 02205.01 4 10Slotted weight, 50 g, coated black 02206.01 4 6Light barrier, compact 11207.20 2 2Portable Blance, OHAUS CS2000 48892.00 1 1Demonstration Track, Aluminium, l = 1.5 m 11305.00 1Cart, low friction sapphire bearings 11306.00 2Starter system for motion track 11309.00 1Weight for low friction cart, 400 g 11306.10 2Shutter plate for low friction cart, w = 100 mm 11308.00 2Holder for light barrier 11307.00 2End holder for demonstration track 11305.12 1Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 2 2Connecting cable, 4 mm plug, 32 A, yellow, l = 100 cm 07363.02 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 2 2Cobra3 BASIC-UNIT, USB 12150.50 1 1Power supply 12V/2A 12151.99 1 1Software Cobra3, Timer/Counter 14511.61 1 1Plasticine, 10 sticks 03935.03 1 1Support rod, stainless steel 18/8, l = 500 mm 02032.00 2Barrel base -PASS- 02006.55 2Bosshead 02043.00 2Stop, adjustable 11202.19 1Connecting cable, 4 mm plug, 32 A, red, l = 10 cm 07359.01 2 2Diaphragm, l = 25 mm 11202.04 2PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of collision with Cobra3 / Air track or Demonstration track P2130511/15

Mechanics Dynamics


� Conservation of momentum� Conservation of energy� Linear motion� Velocity� Elastic loss

Set-up of experiment P2130511 with air track

LEP_1_1 09.08.2007 11:15 Uhr Seite 22


Dynamics Mechanics

Free fall 1.3.07-01

Principle:A sphere falling freely covers certaindistances. The falling time is meas-ured and evaluated from diagrams.The acceleration due to gravity canbe determined.

Height of fall as a function of falling time.

Tasks:1. To determine the functional rela-

tionship between height of falland falling time (h = h(t)=1/2 gt2).

2. To determine the acceleration dueto gravity.


� Linear motion due to constantacceleration

� Laws of falling bodies� Gravitational acceleration

Falling sphere apparatus 02502.88 1

Digital counter, 4 decades 13600.93 1

Alternatively to 13600.93:

Timer 2-1 13607.99 1



Plate holder, opening width 0...10 mm 02062.00 1


Meter Scale, l = 1000 x 27 mm 03001.00 1


Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 2

Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedFree fall P2130701

LEP_1_1 09.08.2007 11:15 Uhr Seite 23

Height of fall as a function of falling time.


1.3.07-11 Free fall with Cobra3

Principle:The fall times t are measured for dif-ferent heights of fall h. h is repre-sented as the function of t or t2, sothe distance-time law of the free fallresults as

h = 1 · g · t2

Then the measured values are takento determine the acceleration due togravity g.

2

Tasks:Determination of:

– Distance time law for the free fall.

– Velocity-time law for the free fall.

– Precise measurement of the accel-eration due to gravity for the freefall.

Falling sphere apparatus 02502.88 1Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 1Software Cobra3, Timer/Counter 14511.61 1Tripod base -PASS- 02002.55 1Support rod -PASS-, square, l = 1000 mm 02028.55 1Right angle clamp -PASS- 02040.55 2Measuring tape, l = 2 m 09936.00 1Connecting cable, 4 mm plug, 32 A, yellow, l = 75 cm 07362.02 1Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 1Connecting cable, 4 mm plug, 32 A, yellow, l = 150 cm 07364.02 1Connecting cable, 4 mm plug, 32 A, blue, l = 150 cm 07364.04 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedFree fall with Cobra3 P2130711

Mechanics Dynamics


� Linear motion due to constantacceleration

� Laws governing falling bodies� Acceleration due to gravity

LEP_1_1 09.08.2007 11:15 Uhr Seite 24


Dynamics Mechanics

Determination of the gravitational constant with a Cavendish balance 1.3.09-01

Principle:Two small lead balls of equal massare positioned one at each end of abeam which is held suspended by athin tungsten thread, so that it canswing freely across its equilibriumposition. When two further, but larg-er, lead balls held on a swivel arm arenow brought near to the small leadballs, forces of attraction resultingfrom gravitation effect accelerationof the small balls in the direction ofthe larger balls. At the same time,the twisted metal thread generates arestoring moment of rotation, so

that the beam is subjected todamped oscillation across a newequilibrium position. The gravita-tional constant can be determinedboth from the difference in the angleof rotation of the different equilibri-um positions and from the dynamicbehaviour of the swinging systemduring attraction.

An integrated capacitive sensor pro-duces a direct voltage that is propor-tional to the angle of deflection. Thiscan be recorded over time by an in-terface system, and the value of theangle of rotation that is required beso determined.

Output voltage of the free and damped oscillating Cavendish balance.

Tasks:1. Calibrate the voltage of the ca-

pacitive angle sensor.

2. Determine the time of oscillationand the damping of the freelyswinging torsion pendulum.

3. Determine the gravitational con-stant, using either the accelera-tion method, the final deflectionmethod or the resonance method.

Cavendish-balance, computerized 02540.00 1

Data cable 2 x SUB-D, plug/socket, 9 pole 14602.00 1

Circular level with mounting, d = 35 mm 02122.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDetermination of the gravitational constant with a Cavendish balance P2130901


� Law of gravitation� Torsional vibrations� Free and damped oscillations� Forced oscillations� Angular restoring moment� Moment of inertia of spheres

and rods� Steiner`s theorem� Shear modulus

LEP_1_1 09.08.2007 11:15 Uhr Seite 25


Mechanics Dynamics

1.3.11-00 Projectile motion

Principle:A steel ball is fired by a spring at dif-ferent velocities and at differentangles to the horizontal. The rela-tionships between the range, theheight of projection, the angle of in-clination, and the firing velocity aredetermined.

Maximum range as a function of the angle of inclination � for different initialvelocity v0: Curve 1 v0 = 5.3 m/s

Curve 2 v0 = 4.1 m/sCurve 3 v0 = 3.1 m/s

Tasks:1. To determine the range as a func-

tion of the angle of inclination.

2. To determine the maximum heightof projection as a function of theangle of inclination.

3. To determine the (maximum)range as a function of the initialvelocity.


� Trajectory parabola� Motion involving uniform

acceleration� Ballistics

Ballistic unit 11229.10 1

Recording paper, 1 roll, 25 m 11221.01 1

Steel ball, hardened and polished, d = 19 mm 02502.01 2

Two tier platform support 02076.03 1

Meter Scale, l = 1000 x 27 mm 03001.00 1


Speed measuring attachment 11229.30 1

Power supply 5 VDC/2.4 A with DC-socket 2.1 mm 13900.99 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedProjectile motion P2131100

LEP_1_1 09.08.2007 11:15 Uhr Seite 26


Dynamics Mechanics

Principle:A classic method of determining thevelocity of a projectile is to shoot theprojectile into a resting mass whichis large compared to the projectile’smass and hung as a pendulum. In theprocess, the projectile remains in thependulum mass and oscillates withit. This is an inelastic collision inwhich the momentum remainsunchanged. If the pendulum’smechanical data are known, one caninfer the velocity of the pendulum’smass (including the projectile’s mass)at the lowest point of thependulum’s oscillation from theamplitude of the pendulum’s oscilla-tion. The momentum of the twomasses in this phase of the oscilla-tion must thus be equal to theimpulse of the projectile before itstruck the pendulum. If one knowsthe masses of the pendulum and theprojectile, one can calculate theprojectile’s velocity.

In order to be able to use this meas-uring principle without danger, thefollowing set-up is used here: A steelball is shot at the mass of a pendu-lum with the aid of a spring catapult.The pendulum mass has a hollowspace in which the steel ball is held.

If, additionally, two light barriers anda time measuring device are avail-able, an independent, direct meas-urement of the initial velocity of theball can be made.

Experimental set-up with supplement for direct measurement of the initialvelocity of the ball.

Tasks:1. Measurement of the oscillation

amplitudes of the ballistic pendu-lum after capturing the steel ballfor the three possible tensionenergies of the throwing device.

2. Calculation of the initial velocitiesof the ball from the measuredoscillation amplitudes and themechanical data of the pendulumis performed using the approxima-tion formula (3).

3. Plotting of the velocity v of thesteel ball as a function of themaximum deflection � (0…90°) ofthe pendulum according to for-mula (3), taking into considerationthe special mechanical data of theexperiment.

4. Determination of the correctionfactor fcor for the utilised pendu-lum for the conversion of thevelocities determined by using theapproximation formula into thevalues obtained from the exacttheory. Correction of the velocityvalues from Tasks 2.

5. If the supplementary devices forthe direct measurement of theinitial velocity are available,measure the initial velocities cor-responding to the three tensionsteps of the throwing device byperforming 10 measurementseach with subsequent mean valuecalculation. Plot the measuredpoints in the diagram from Task 3.Give reasons for contingentsystematic deviations from thetheoretical curve.

Ballistic unit 11229.10 1

Ballistic pendulum f. ballistic unit 11229.20 1

Speed measuring attachment 11229.30 1

Steel ball, hardened and polished, d = 19 mm 02502.01 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedBallistic Pendulum P2131200


� Potential and kinetic energy� Rotational energy� Moment of inertia� Inelastic collision� Principle of conservation of

momentum� Angular momentum� Measurement of projectile

velocities

Ballistic Pendulum 1.3.12-00

LEP_1_1 09.08.2007 11:15 Uhr Seite 27

1.3.13-01/05 Moment of inertia and angular acceleration

Principle:A moment acts on a body which canbe rotated about a bearing withoutfriction. The moment of inertia isdetermined from the angular accel-eration.

Moment of inertia of a mass point as a function of the square of its distancefrom the axis of rotation.

Tasks:From the angular acceleration, themoment of inertia is determined as a function of the mass and of thedistance from the axis of rotation.

1. of a disc,

2. of a bar,

3. of a mass point.


� Angular velocity� Rotary motion� Moment� Moment of inertia of a disc� Moment of inertia of a bar� Moment of inertia of a mass

point

Experiment P2131305 with precision pivot bearingExperiment P2131301 with air bearingTripod base -PASS- 02002.55 2 1Precision pivot bearing 02419.00 1Inertia rod 02417.03 1 1Turntable with angular scale 02417.02 1 2Aperture plate for turntable 02417.05 1 1Air bearing 02417.01 1Holding device with cable release 02417.04 1 1Precision pulley 11201.02 1 1Blower 230 V/50Hz 13770.97 1Pressure tube, l = 1.5 m 11205.01 1Light barrier with counter 11207.30 1 1Power supply 5 V DC/2.4 A with 4 mm plugs 11076.99 1 1Supporting blocks, 10, 20, 30, 40 mm 02070.00 1Slotted weights, 1 g, polished 03916.00 20 20Slotted weights, 10 g, coated black 02205.01 10 10Slotted weight, 50 g, coated black 02206.01 2 2Weight holder, 1g, silver bronzing 02407.00 1 1Silk thread on spool, l = 200 mm 02412.00 1 1Support rod -PASS-, square, l = 1000 mm 02028.55 1Support rod -PASS-, square, l = 400 mm 02026.55 1 1Right angle clamp -PASS- 02040.55 3 2Bench clamp -PASS- 02010.00 2 2Connecting cord, 32 A, 1000 mm, red 07363.01 1Connecting cord, 32 A, 1000 mm, blue 07363.04 1Adapter, BNC-plug/socket 4 mm. 07542.26 1Capacitor 100 nF/250V, G1 39105.18 1Circular level 02122.00 1Weight holder for slotted weights 02204.00 1Measuring tape, l = 2 m 09936.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment of inertia and angular acceleration P2131301/05


Mechanics Dynamics

Set-up of experiment P2131305 with pivot bearing

LEP_1_1 09.08.2007 11:15 Uhr Seite 28


Dynamics Mechanics

Moment of inertia and angular acceleration with Cobra3 1.3.13-11/15

Principle:If a constant torque is applied to abody that rotates without frictionaround a fixed axis, the changingangle of rotation increases propor-tionally to the square of the time andthe angular velocity proportional tothe time.

Potential energy and additionally the rotational energy.

Tasks:1. Measurement of the laws of angle

and angular velocity according totime for a uniform rotation move-ment.

2. Measurement of the laws of angleand angular velocity according totime for a uniformly acceleratedrotational movement.

3. Rotation angle � is proportional tothe time t required for the rota-tion.

Experiment P2131315 with precision pivot bearingExperiment P2131311 with air bearingCobra3 BASIC-UNIT, USB 12150.50 1 1Tripod base -PASS- 02002.55 1 1Precision pivot bearing 02419.00 1Inertia rod 02417.03 1Power supply 12V/2A 12151.99 1 1Software Cobra3, Translation/ Rotation 14512.61 1 1Light barrier, compact 11207.20 1 1Blower 230V/50Hz 13770.97 1Pressure tube, l = 1.5 m 11205.01 1Air bearing 02417.01 1Turntable with angular scale 02417.02 1 1Holding device with cable release 02417.04 1 1Aperture plate for turntable 02417.05 1 1Slotted weights, 1 g, polished 03916.00 9 20Slotted weights, 10 g, coated black 02205.01 3 10Slotted weight, 50 g, coated black 02206.01 2 2Silk thread on spool, l = 200 mm 02412.00 1 1Weight holder for slotted weights 02204.00 1 1Bench clamp -PASS- 02010.00 2 2Stand tube 02060.00 1Support rod, stainless steel 18/8, l = 250 mm, d = 10 mm 02031.00 1 1Measuring tape, l = 2 m 09936.00 1 1Circular level with mounting, d = 35 mm 02122.00 1 1Bosshead 02043.00 1 1Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 1 1Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 1 1Connecting cable, 4 mm plug, 32 A, yellow, l = 100 cm 07363.02 1 1Data cable, plug/socket, 9 pole 14602-00 1Weight holder, 1 g 02407-00 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment of inertia and angular accelerationwith Cobra3 P2131311/15


� Angular velocity� Rotation� Moment� Torque� Moment of inertia� Rotational energy

Set-up of experiment P2131311 with air bearing

LEP_1_1 09.08.2007 11:15 Uhr Seite 29

1.3.15-00 Moment and angular momentum

Principle:The angle of rotation and angularvelocity are measured as a functionof time on a body which is pivoted soas to rotate without friction andwhich is acted on by a moment. Theangular acceleration is determinedas a function of the moment.

3. the angular acceleration as afunction of time,

4. the angular acceleration as afunction of the lever arm.

Angle of rotation as a function of time with uniformly accelerated rotarymotion for m = 0.01 kg, r = 0.015 m.

Tasks:With uniformly accelerated rotarymotion, the following will be deter-mined:

1. the angle of rotation as a functionof time,

2. the angular velocity as a functionof time.


� Circular motion� Angular velocity� Angular acceleration� Moment of inertia� Newton’s laws� Rotation

Turntable with angular scale 02417.02 1

Aperture plate for turntable 02417.05 1

Holding device with cable release 02417.04 1

Air bearing 02417.01 1

Precision pulley 11201.02 1

Pressure tube, l = 1.5 m 11205.01 1

Blower 230V/50Hz 13770.97 1

Light barrier with counter 11207.30 1

Power supply 5 V DC/2.4 A with 4 mm plugs 11076.99 1

Capacitor 100 nF/250 V, G1 39105.18 1

Adapter, BNC plug/4 mm socket 07542.26 1

Weight holder, 1 g, silver bronzing 02407.00 1

Slotted weights, 1 g, polished 03916.00 20




Circular level with mounting, d = 35 mm 02122.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment and angular momentum P2131500


Mechanics Dynamics

LEP_1_1 09.08.2007 11:15 Uhr Seite 30


Dynamics Mechanics

Centrifugal force 1.3.16-01

Principle:A body with variable mass moves ona circular path with adjustable radiusand variable angular velocity. Thecentrifugal force of the body will bemeasured as a function of theseparameters.

Centrifugal force as a function of the angular velocity v.

Tasks:Determination of the centrifugalforce as a function

1. of the mass,

2. of the angular velocity,

3. of the distance from the axis ofrotation to the centre of gravity ofthe car.

Centrifugal force apparatus 11008.00 1

Car for measurements and experiments 11060.00 1


Laboratory motor, 220 VAC 11030.93 1

Gearing 30:1 11029.00 1

Bearing unit 02845.00 1

Driving belt 03981.00 1

Support rod with hole, stainless steel, l = 10 cm 02036.01 1



Spring balance holder 03065.20 1


Bosshead 02043.00 2



Transparent spring balances, 2 N 03065.03 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedCentrifugal force P2131601


� Centripetal force� Rotary motion� Angular velocity� Apparent force

LEP_1_1 09.08.2007 11:15 Uhr Seite 31

1.3.16-11 Centrifugal force with Cobra3

Principle:A body with variable mass moves ona circular path with adjustable radiusand variable angular velocity. Thecentrifugal force of the body will bemeasured as a function of these pa-rameters.

Typical evaluation of central force as a function of the square of angularvelocity.

Tasks:Determination of the centrifugalforce as a function

1. of the mass,

2. of the angular velocity,

3. of the distance from the axis ofrotation to the centre of gravity ofthe car.


� Centrifugal force� Centripetal force� Rotary motion� Angular velocity� Apparent force


Power supply 12V/2A 12151.99 1

Newton measuring module 12110.00 1

Newton Sensor 12110.01 1

Software Cobra3 Force/Tesla 14515.61 1

Centrifugal force apparatus 11008.00 1

Car for measurements and experiments 11060.00 1



Gearing 30:1 11029.00 1











What you need:

Complete Equipment Set, Manual on CD-ROM includedCentrifugal force with Cobra3 P2131611


Mechanics Dynamics

LEP_1_1 09.08.2007 11:15 Uhr Seite 32


Dynamics Mechanics

Mechanical conservation of energy / Maxwell’s wheel 1.3.18-00

Principle:A disk, which can unroll with its axison two cords, moves in the gravita-tional field. Potential energy, energyof translation and energy of rotationare converted into one another andare determined as a function of time.

Energy of the Maxwell disk as afunction of time.1. Negative potential energy2. Energy of translation3. Energy of rotation

Tasks:The moment of inertia of theMaxwell disk is determined.

Using the Maxwell disk,

1. the potential energy,

2. the energy of translation,

3. the energy of rotation,

are determined as a function of time.




Meter Scale, l = 1000 x 27 mm 03001.00 1


Maxwell wheel 02425.00 1




Holding device with cable release 02417.04 1



Capacitor 100 nF/250 V, G1 39105.18 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedMechanical conservation of energy /Maxwell’s wheel P2131800


� Maxwell disk� Energy of translation� Energy of rotation� Potential energy� Moment of inertia� Angular velocity� Angular acceleration� Instantaneous velocity� Gyroscope

LEP_1_1 09.08.2007 11:15 Uhr Seite 33

1.3.19-00 Laws of gyroscopes / 3-axis gyroscope

Principle:The momentum of inertia of thegyroscope is investigated by measur-ing the angular acceleration causedby torques of different known values.In this experiment, two of the axes ofthe gyroscope are fixed.

The relationship between the preces-sion frequency and the gyro-fre-quency of the gyroscope with 3 freeaxes is examined for torques of dif-ferent values applied to the axis ofrotation.

If the axis of rotation of the force-free gyroscope is slightly displaced, anutation is induced. The nutationfrequency will be investigated as afunction of gyro-frequency.

3. Investigation of the relationshipbetween precession and gyro-fre-quency and its dependence fromtorque.

4. Investigation of the relationshipbetween nutation frequency andgyro-frequency.

Determination of the momentum of inertia from the slope of straight line tR

-1 = f(tP).

Tasks:1. Determination of the momentum

of inertia of the gyroscope bymeasurement of the angularacceleration.

2. Determination of the momentumof inertia by measurement of thegyro-frequency and precessionfrequency.


� Momentum of inertia� Torque� Angular momentum� Precession� Nutation


Mechanics Dynamics

Gyroscope with 3 axis 02555.00 1



Additional gyro disk with counter weight 02556.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of gyroscopes / 3-axis gyroscope P2131900

LEP_1_1 09.08.2007 11:15 Uhr Seite 34


Dynamics Mechanics

Laws of gyroscopes / cardanic gyroscope 1.3.20-00

Principle:If the axis of rotation of the forcefreegyroscope is displaced slightly, a nu-tation is produced. The relationshipbetween precession frequency or nu-tation frequency and gyro-frequencyis examined for different moments ofinertia.

Additional weights are applied to agyroscope mounted on gimbals, socausing a precession.

Precession frequency as a function of the gyro frequency for different addi-tional masses.

Tasks:1. To determine the precession fre-

quency as a function of the torqueand the angular velocity of thegyroscope.

2. To determine the nutational fre-quency as a function of the an-gular velocity and the moment ofinertia.

Gyroscope, Magnus type, incl. Handbook 02550.00 1


Digital stroboscope 21809.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of gyroscopes / cardanic gyroscope P2132000


� Moment of inertia� Torque� Angular momentum� Nutation� Precession� Chaotic behaviour

1. m2 = 0.163 kg

2. m2 – m1 = 0.112 kg

3. m1 = 0.051 kg

Note:A detailed handbook (128 pages)containing additional experiments isincluded, free of charge, in theequipment.

LEP_1_1 09.08.2007 11:15 Uhr Seite 35

1.3.21-00 Mathematical pendulum

Principle:A mass, considered as of point form,suspended on a thread and subjectedto the force of gravity, is deflectedfrom its position of rest. The periodof the oscillation thus produced ismeasured as a function of the threadlength and the angle of deflection.

Period of the pendulum as a function of the angle of deflection.

Tasks:1. For small deflections, the oscilla-

tion period is determined as afunction of the cord length.

2. The acceleration due to gravity isdetermined.

3. The oscillation period is deter-mined as a function of the deflec-tion.


� Duration of oscillation� Period� Amplitude� Harmonic oscillation



Steel balls with eyelet, d = 25.4 mm 02465.01 1

Steel balls with eyelet, d = 32 mm 02466.01 1

Meter Scale, l = 1000 x 27 mm 03001.00 1




Clamping pads on stem 02050.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedMathematical pendulum P2132100


Mechanics Dynamics

LEP_1_1 09.08.2007 11:15 Uhr Seite 36


Dynamics Mechanics

Reversible pendulum 1.3.22-00

T2

S

1.50

1.56

1.42

1.38

1.34

1.30

X

X

X

X

X

X X XX

X

X

X

X

30 40 50 60

�'a �'min �'s �'cm

Principle:By means of a reversible pendulum,terrestrial gravitational accelerationg may be determined from the peri-od of oscillation of a physical pendu-lum, knowing neither the mass northe moment of inertia of the latter.

Period T2 as a function of the position of the axis of rotation of the physicalpendulum.

Tasks:1. Measurement of the period for

different axes of rotation.

2. Determination of terrestrial gravi-tational acceleration g.

Bearing bosshead for reversing pendulum 02805.00 2

Support rod, stainless steel, l = 750 mm 02033.00 1

Bolt with knife edge 02049.00 2








What you need:

Complete Equipment Set, Manual on CD-ROM includedReversible pendulum P2132200


� Physical pendulum� Moment of inertia� Steiner’s law� Reduced length of pendulum� Reversible pendulum� Terrestrial gravitational

acceleration

LEP_1_1 09.08.2007 11:15 Uhr Seite 37

1.3.23-01 Pendulum oscillations / variable g pendulum

Principle:Investigate the oscillation behaviourof a pendulum (rod pendulum) byvarying the magnitude of the com-ponents of the acceleration of grav-ity which are decisive for the oscilla-tion period. The pendulum that is tobe used is constructed in such amanner that its oscillation plane canbe progressively rotated from a ver-tical orientation to a horizontal one.The angle F, by which the oscillationplane deviates from its normal ver-tical position, can be read from ascale.

Oscillation period of the pendulumas a function of the slope �. of theoscillation plane. The measuredpoints are plotted above the corre-sponding theoretical curve (solidline). Upper curve: L = 270 mm;lower curve: L = 141 mm.

Tasks:1. Measurement of the oscillation

period of the pendulum as a func-tion of the angle of inclination �of the oscillation plane for twodifferent pendulum lengths.

2. Graphical analysis of the meas-ured correlations and a compari-son with the theoretical curves,which have been standardisedwith the measured value at � = 0.

3. Calculation of the effective pen-dulum length l for the accelera-tion of gravity, which is assumedto be known. Comparison of thisvalue with the distance betweenthe pivot point of the pendulumand the centre of gravity of themobile pendulum weight.

4. On the moon’s surface the “lunaracceleration of gravity” gm is only16.6% of the earth’s accelerationof gravity g. Calculate the angle �and set it on the device such thatthe pendulum in the laboratoryoscillates with the same oscilla-tion period with which it wouldoscillate on the moon in a perpen-dicular position. Compare themeasured oscillation period withthe calculated one.


� Oscillation period� Harmonic oscillation� Mathematical pendulum� Physical pendulum� Decomposition of force� Moment of inertia

Variable g-pendulum 02817.00 1

Holder for light barrier 02817.10 1

Light barrier, compact 11207.20 1

Timer 4-4 13605.99 1

Alternatively to 13605.99:

Timer 2-1 13607.99 1



Connecting cable, 4 mm plug, 32 A, yellow, l = 50 cm 07361.02 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedPendulum oscillations /variable g pendulum P2132301


Mechanics Dynamics

LEP_1_1 09.08.2007 11:15 Uhr Seite 38


Dynamics Mechanics

Pendulum oscillations with Cobra3 1.3.23-11

Principle:Earth’s gravitational acceleration g isdetermined for different lengths ofthe pendulum by means of the oscil-lating period. If the oscillating planeof the pendulum is not parallel to thegravitational field of the earth, onlyone component of the gravitationalforce acts on the pendulum move-ment.

Typical measurement result

Tasks:1. Determination of the oscillation

period of a thread pendulum as afunction of the pendulum length.

2. Determination of g.

3. Determination of the gravitation-al acceleration as a function ofthe inclination of the pendulumforce.

Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 1Software Cobra3, Translation/ Rotation 14512.61 1Movement sensor with cable 12004.10 1Adapter BNC socket/4 mm plug pair 07542.27 1Adapter, BNC socket - 4 mm plug 07542.20 1Silk thread on spool, l = 200 mm 02412.00 1Fishing line on spool, d = 0,7 mm, l = 20 mm 02089.00 1Weight holder, 1g, silver bronzing 02407.00 1Steel balls with eyelet, d = 32 mm 02466.01 2Tripod base -PASS- 02002.55 1Support rod -PASS-, square, l = 1000 mm 02028.55 1Stand tube 02060.00 1Plate holder, opening width 0...10 mm 02062.00 1Right angle clamp -PASS- 02040.55 2Bench clamp -PASS- 02010.00 1Protractor scale with pointer 08218.00 1Circular level with mounting, d = 35 mm 02122.00 1Measuring tape, l = 2 m 09936.00 1Pendulum 12004.11 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedPendulum oscillations with Cobra3 P2132311


� Oscillation period� Harmonic oscillation� Mathematical pendulum� Physical pendulum� Variable g-pendulum� Decomposition of force� Gravitational force

LEP_1_1 09.08.2007 11:15 Uhr Seite 39


1.3.25-01 Coupled Pendula

Principle:Two equal gravity pendula with aparticular characteristic frequencyare coupled by a “soft” spiral spring.The amplitudes of both pendula arerecorded as a function of time forvarious vibrational modes and differ-ent coupling factors using a y/trecorder. The coupling factors aredetermined by different methods.

Tasks:1. To determine the spring constant

of the coupling spring.

2. To determine and to adjust thecharacteristic frequencies of theuncoupled pendula.

3. To determine the coupling factorsfor various coupling-lengths using

a) the apparatus constants

b) the angular frequencies for“inphase” and “in oppositephase” vibration

c) the angular frequencies of thebeat mode.

4. To check the linear relationbetween the square of thecoupling-lengths and

a) the particular frequencies ofthe beat mode

b) the square of the frequency for“in opposite phase” vibration.

5. To determine the pendulum’scharacteristic frequency from thevibrational modes with couplingand to compare this with thecharacteristic frequency of theuncoupled pendula.

Pendulum with recorder connection 02816.00 2


Rod with hook 02051.00 1



Yt recorder, 2 channels 11415.95 1

Power supply 0-12 V DC/ 6 V, 12 V AC 13505.93 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedCoupled Pendula P2132501

Mechanics Dynamics


� Spiral spring� Gravity pendulum� Spring constant� Torsional vibration� Torque� Beat� Angular velocity� Angular acceleration� Characteristic frequency

Amplitude curves of the vibrations ofcoupled pendula in the beat case forthree different coupling lengths l asa function of time.Speed of recorder: t = 10 s/Div.

l = 30 cm

l = 60 cm

l = 90 cm

LEP_1_1 09.08.2007 11:15 Uhr Seite 40


Coupled Pendula with Cobra3 1.3.25-11

Dynamics Mechanics

Principle:Two equal gravity pendula with aparticular characteristic frequencyare coupled by a “soft” spiral spring.The amplitudes of both pendula arerecorded as a function of time forvarious vibrational modes and differ-ent coupling factors using a y/trecorder. The coupling factors aredetermined by different methods.

Tasks:1. To determine the spring constant

of the coupling spring.

2. To determine and to adjust thecharacteristic frequencies of theuncoupled pendula.

3. To determine the coupling factorsfor various coupling-lengths using

a) the apparatus constants

b) the angular frequencies for“inphase” and “in oppositephase” vibration

c) the angular frequencies of thebeat mode.

4. To check the linear relation be-tween the square of the coupling-lengths and

a) the particular frequencies ofthe beat mode

b) the square of the frequency for“in opposite phase” vibration.

5. To determine the pendulum’scharacteristic frequency from thevibrational modes with couplingand to compare this with thecharacteristic frequency of theuncoupled pendula.


� Spiral spring� Gravity pendulum� Spring constant� Torsional vibration� Torque� Beat� Angular velocity� Angular acceleration� Characteristic frequency

Pendulum with recorder connection 02816.00 2Helical springs, 3 N/m 02220.00 1Rod with hook 02051.00 1Weight holder for slotted weights 02204.00 1Slotted weights, 10 g, coated black 02205.01 5Electrolyte capacitors G1, 10 µF 39105.28 2Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 1Software Cobra3 Universal recorder 14504.61 1Power supply 0-12 V DC/ 6 V, 12 V AC 13505.93 1Bench clamp -PASS- 02010.00 2Support rod -PASS-, square, l = 630 mm 02027.55 2Right angle clamp -PASS- 02040.55 2Measuring tape, l = 2 m 09936.00 1Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 4Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 4PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedCoupled Pendula with Cobra3 P2132511

l = 30 cm

l = 60 cm

l = 90 cm

Amplitude curves of the vibrations ofcoupled pendula in the beat case forthree different coupling lengths l (30 cm, 60 cm and 90 cm) as afunction of time.

LEP_1_1 09.08.2007 11:15 Uhr Seite 41

1.3.26-11 Harmonic oscillations of spiral springs – Springs linked in parallel and series

Principle:The spring constant D is determinedfor different experimental set-upsfrom the oscillation period and thesuspended mass.

Typical measurement result

Tasks:1. Determination of the spring con-

stant D for different springs.

2. Determination of the spring con-stant for springs linked in parallel.

3. Determination of the spring con-stant for springs linked in series.


� Spring constant� Hooke’s law oscillations� Limit of elasticity� Parallel springs� Serial springs� Use of an interface



Software Cobra3, Translation/ Rotation 14512.61 1








Stand tube 02060.00 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedHarmonic oscillations of spiral springs –Springs linked in parallel and series P2132611


Mechanics Dynamics

LEP_1_1 09.08.2007 11:15 Uhr Seite 42


Dynamics Mechanics

Forced Oscillations – Pohl’s pendulum 1.3.27-01

Principle:If an oscillating system is allowed toswing freely it is observed that thedecrease of successive maximumamplitudes is highly dependent onthe damping. If the oscillatingsystem is stimulated to swing by an

B. Forced oscillation

1. The resonance curves are to bedetermined and to be repre-sented graphically using thedamping values of A.

2. The resonance frequencies areto be determined and are to becompared with the resonancefrequency values found before-hand.

3. The phase shifting between thetorsion pendulum and the stim-ulating external torque is to beobserved for a small dampingvalue assuming that in one casethe stimulating frequency is farbelow the resonance frequencyand in the other case it is farabove it.

Resonance curves for different dampings.

Tasks:A. Free oscillation

1. To determine the oscillatingperiod and the characteristicfrequency of the undampedcase.

2. To determine the oscillatingperiods and the correspondingcharacteristic frequencies fordifferent damping values. Suc-cessive, unidirectional maxi-mum amplitudes are to be plot-ted as a function of time. Thecorresponding ratios of attenu-ation, the damping constantsand the logarithmic decrementsare to be calculated.

3. To realize the aperiodic caseand the creeping.

Torsion pendulum after Pohl 11214.00 1

Power supply, universal 13500.93 1

Bridge rectifier, 30 VAC/1 ADC 06031.10 1


Digital multimeter 2010 07128.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedForced Oscillations – Pohl’s pendulum P2132701


� Angular frequency� Characteristic frequency� Resonance frequency� Torsion pendulum� Torsional vibration� Torque and Restoring torque� Damped/undamped free

oscillation� Forced oscillation� Ratio of attenuation/

decrement� Damping constant� Logarithmic decrement� Aperiodic case� Creeping

external periodic torque, we observethat in the steady state the ampli-tude is a function of the frequencyand the amplitude of the externalperiodic torque and of the damping.The characteristic frequencies of thefree oscillation as well as the reso-nance curves of the forced oscilla-tion for different damping values areto be determined.

LEP_1_1 09.08.2007 11:15 Uhr Seite 43


Mechanics Dynamics

1.3.27-11 Forced Oscillations – Pohl’s pendulumDetermination of resonance frequencies by Fourier analysis

Principle:If an oscillating system is allowed toswing freely it is observed that thedecrease of successive maximumamplitudes is highly dependent onthe damping. If the oscillatingsystem is stimulated to swing by anexternal periodic torque, we observethat in the steady state the ampli-tude is a function of the frequencyand the amplitude of the externalperiodic torque and of the damping.The characteristic frequencies of the

rectional maximum amplitudes areto be plotted as a function of time.The corresponding ratios of attenua-tion, the damping constants and thelogarithmic decrements are to becalculated.

3. To realize the aperiodic case andthe creeping.

Tasks:A. Free oscillation1. To determine the oscillating peri-

od and the characteristic frequen-cy of the undamped case.

2. To determine the oscillating peri-ods and the corresponding char-acteristic frequencies for differentdamping values. Successive, unidi-


� Angular frequency� Characteristic frequency� Resonance frequency� Torsion pendulum� Torsional vibration� Torque� Testoring torque� Damped/undamped free

oscillation� Forced oscillation� Ratio of attenuation/

decrement� Damping constant� Logarithmic decrement� Aperiodic case� Creeping� Chaotic behaviour

Torsion pendulum after Pohl 11214.00 1


Bridge rectifier, 30 VAC/1 ADC 06031.10 1









Movement sensor with cable 12004.10 1

Adapter BNC socket/4 mm plug pair 07542.27 1

Adapter, BNC socket - 4 mm plug 07542.20 1


Weight holder, 1g, silver bronzing 02407.00 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedForced Oscillations – Pohl’s pendulumDetermination of resonance frequencies by Fourier analysis P2132711

Recorded curve of the damped oscillation.

B. Forced oscillation1. The resonance curves are to be

determined and to be representedgraphically using the dampingvalues of A.

2. The resonance frequencies are tobe determined and are to be com-pared with the resonance fre-quency values found beforehand.

free oscillation as well as the reso-nance curves of the forced oscilla-tion for different damping values areto be determined.Therefore, the oscillations arerecorded with the Cobra3 systeminconnection with the movement sen-sor. The curves of the different oscil-lations are displayed and the neces-sary quantities for the determinationof the characteristic values can eas-ily becalculated.

3. The phase shifting between thetorsion pendulum and the stimu-lating external torque is to beobserved for a small dampingvalue assuming that in one casethe stimulating frequency is farbelow the resonance frequencyand in the other case it is farabove it.

LEP_1_1 09.08.2007 11:15 Uhr Seite 44


Dynamics Mechanics

Moment of inertia / Steiner’s theorem 1.3.28-01

Principle:The period of vibration of a circulardisc which performs torsional vibra-tions about various parallel axes, ismeasured. The moment of inertia ofthe disc is determined as a functionof the perpendicular distance of theaxis of rotation from the centre ofgravity.

Moment (torque) of a spiral spring as a function of the angle of rotation.

Tasks:1. Determination of the angular

restoring constant of the spiralspring.

2. Determination of the moment ofinertia of a circular disc as a func-tion of the perpendicular distanceof the axis of rotation from thecentre of gravity.

Rotation axle 02415.01 1

Disk with diametrical holes 02415.07 1

Transparent spring balances, 2 N 03065.03 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment of inertia / Steiner’s theorem P2132801


� Rigid body� Moment of inertia� Centre of gravity� Axis of rotation� Torsional vibration� Spring constant� Angular restoring force

LEP_1_1 09.08.2007 11:15 Uhr Seite 45


Mechanics Dynamics

1.3.28-11 Moments of inertia of different bodies / Steiner’s theorem with Cobra3

Principle:The moment of inertia of a solid bodydepends on its mass distribution andthe axis of rotation. Steiner’s theo-rem elucidates this relationship.

Typical measuring result

Tasks:The moments of inertia of differentbodies are determined by oscillationmeasurements. Steiner’s theorem isverified.


� Rigid body� Moment of inertia� Centre of gravity� Axis of rotation� Torsional vibration� Spring constant� Angular restoring force





Angular oscillation apparatus 02415.88 1

Portable Blance, OHAUS CS2000 48892.00 1

Flat cell battery, 9 V 07496.10 1












What you need:

Complete Equipment Set, Manual on CD-ROM includedMoments of inertia of different bodies /Steiner’s theorem with Cobra3 P2132811

LEP_1_1 09.08.2007 11:15 Uhr Seite 46


Dynamics Mechanics

Torsional vibrations and torsion modulus 1.3.30-00

Principle:Bars of various materials will be ex-citing into torsional vibration. Therelationship between the vibrationperiod and the geometrical dimen-sions of the bars will be derived andthe specific shear modulus for thematerial determined.

Torque and deflection of a torsion bar.

Tasks:1. Static determination of the tor-

sion modulus of a bar.

2. Determination of the moment ofinertia of the rod and weightsfixed to the bar, from the vibrationperiod.

3. Determination of the dependenceof the vibration period on thelength and thickness of the bars.

4. Determination of the shear modu-lus of steel, copper, aluminiumand brass.

Torsion apparatus 02421.00 1Torsion rod, steel, d = 2 mm, l = 500 mm 02421.01 1Torsion rod, Al, d = 2 mm, l = 500 mm 02421.02 1Torsion rod, Al, d = 2 mm, l = 400 mm 02421.03 1Torsion rod, Al, d = 2 mm, l = 300 mm 02421.04 1Torsion rod, Al, d = 3 mm, l = 500 mm 02421.05 1Torsion rod, Al, d = 4 mm, l = 500 mm 02421.06 1Torsion rod, brass, d = 2 mm, l = 500 mm 02421.07 1Torsion rod, copper, d = 2 mm, l = 500 mm 02421.08 1Precision spring balance 1 N 03060.01 1Precision spring balances, 2.5 N 03060.02 1Stopwatch, digital, 1/100 s 03071.01 1Sliding weight 03929.00 2Support base -PASS- 02005.55 1Support rod -PASS-, square, l = 250 mm 02025.55 1Support rod -PASS-, square, l = 630 mm 02027.55 1Right angle clamp -PASS- 02040.55 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedTorsional vibrations and torsion modulus P2133000


� Shear modulus� Angular velocity� Torque� Moment of inertia� Angular restoring torque� G-modulus� Modulus of elasticity

LEP_1_2 09.08.2007 11:35 Uhr Seite 47


Principle:Various bodies perform torsionalvibrations about axes through theircentres of gravity. The vibrationperiod is measured and the momentof inertia determined from this.

Moment of inertia of two equal masses, of 0.214 kg each, as a function of thedistance between them.

Tasks:The following will be determined:

1. The angular restoring moment ofthe spiral spring.

2. The moment of inertia

a) of a disc, two cylinder, a sphereand a bar,

b) of two point masses, as a func-tion of the perpendicular dis-tance to the axis of rotation.The centre of gravity lies in theaxis of rotation.


� Rigid body� Moment of inertia� Axis of rotation� Torsional vibration� Spring constant� Angular restoring moment� Moment of inertia of a

sphere� Moment of inertia of a disc� Moment of inertia of a

cylinder� Moment of inertia of a long

bar� Moment of inertia of 2 point

masses

Rotation axle 02415.01 1

Sphere 02415.02 1

Disk 02415.03 1

Hollow cylinder 02415.04 1

Solid cylinder 02415.05 1

Rod with movable masses 02415.06 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment of inertia and torsional vibrations P2133100


Mechanics Dynamics

LEP_1_2 09.08.2007 11:35 Uhr Seite 48


Dynamics Mechanics

The propagation of a periodically excited continuous transverse wave 1.3.32-00

Principle:The periodicity of connected station-ary oscillators is demonstrated onthe example of a continuous, har-monic transverse wave generated bya wave machine. The number ofoscillations carried out by differentoscillators within a certain time isdetermined and the velocity of prop-agation is measured. A relation be-tween frequency, wavelength andphase velocity is established. Theformation of standing waves isdemonstrated and studied.

3. For three different frequencies thecorresponding wavelengths are tobe measured and it is to be shownthat the product of frequency andwavelength is a constant.

4. The four lowest natural frequen-cies with two ends of the oscilla-tor system fixed are to be detect-ed.

5. The four lowest natural frequen-cies with one end of the oscillatorsystem fixed and the other onefree are to be detected.

The resonance frequencies measured with increasing speed of rotation.

Tasks:1. The frequency of the oscillators 1,

10, 20, 30 and 40 is to be deter-mined with the electronic counterof the light barrier and the stop-watch for a particular frequencyof excitation.

2. By means of a path-time mea-surement the phase velocity of atransverse wave is to be deter-mined.

Wave machine 11211.00 1

Dual power supply 2 x 15 V-/ 2 A 13520.93 1




Gearing 30:1 11029.00 1

Gearing 100:1 11027.00 1

Stopwatch, 15 minutes 03076.01 1

Screened cable, BNC, l = 1500 mm 07542.12 1


Meter Scale, l = 1000 x 27 mm 03001.00 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedThe propagation of a periodically excitedcontinuous transverse wave P2133200


� Periodic motion� Frequency� Wavelength� Phase velocity� Standing waves� Natural frequency� Free and fixed end� Damping of waves

fk kf k �

Hz k

0.38 1 0.38 2L/1

0.74 2 0.37 2L/2

0.94 3 0.31 2L/3

1.43 4 0.36 2L/4

LEP_1_2 09.08.2007 11:35 Uhr Seite 49


Principle:A quadrangular rubber rope is insert-ed through the demonstration motorand a linear polarised fixed wave isgenerated. With the help of a strob-oscope, the frequency and the wavelength are determined. Then thephase velocity of rope waves with afixed tensile stress is ascertained.Subsequently, the mathematicalrelationship between the phasevelocity of the rope and the tensileon the rope is examined.

The square of phase velocity depending upon the force F applied on the rope.

Tasks:1. With constant tensile stress, the

frequency f, which depends onthe wavelength � of the wavethat propagates itself along therope. The frequency is plotted as afunction of 1/�. From this graph,the phase velocity c is deter-mined.

2. The phase velocity c of the ropewaves, which depends on the ten-sile stress on the rope is to bemeasured. The quadrant of thephase velocity is plotted as afunction of tensile stress.


� Wavelength� Phase velocity� Group velocity� Wave equation� Harmonic wave

Grooved wheel after Hoffmann 02860.00 1

Square section rubber strip, l = 10 m 03989.00 1


Gearing 10:1 11028.00 1

Cotton cord, d = 2,5 mm, l = 10 mm 02091.00 1






Pulleys, fixed, on rod, d = 10 mm 02260.00 1





Digital stroboscopes 21809.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedPhase velocity of rope waves P2133300


Mechanics Dynamics

LEP_1_2 09.08.2007 11:35 Uhr Seite 50


Wave phenomena in a ripple tank 1.3.34-00

Dynamics Mechanics

Principle:In the ripple tank water waves aregenerated by a vibration generator.Circular waves are then used to in-vestigate the dependency of thevibration frequency on the wavelength. With the aid of plane wavesthe dependency of the velocity of thewaves' propagation on the depth ofthe water can be determined. More-over, the reflection of waves as wellas the refraction of waves at a plate,a prism, a concave lens and at a con-vex lens can be clearly demonstrat-ed. It is shown, that water waves area proved method to demonstrate thebehaviour of waves in general.

3. Plane waves are generated withthe integrated wave generator. Byusing two barriers show the re-flection of waves.

4. Use a plate to simulate a zone oflower water depth and measurethe wave length before and abovethe plate.

5. Observe the refraction of waterwaves at several objects (plate,prism, concave and convex lens).

Examination of the behaviour of a concave lens with the ripple tank.

Tasks:1. Use the single dipper to generate

circular waves. By using a rulerthe wave length can be deter-mined. The measurement is madefor different frequencies.

2. The external wave generator isconnected to the water ripple tankand circular waves are generated.By moving the external wave gen-erator the Doppler Effect is inves-tigated.


� Generation of surface waves� Propagation of surface waves� Dependency of wave velocity� Reflection of waves� Refraction of waves� Concave, convex lenses,

mirrors

Ripple tank with LED-light source , complete 11260.99 1

Optional equipment for demonstration purposes in classes or lectures:

Demo set for ripple tank (USB-Camera, Fixing unit) 11260.20 1


or

Demo set with mirror for ripple tank 11260.30 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedWave phenomena in a ripple tank P2133400

LEP_1_2 09.08.2007 11:35 Uhr Seite 51



Principle:Different types of circular waterwaves are generated simultaneously.The resulting interference is ob-served. By increasing the number ofcircular waves which interfere Huy-gens' Principle can be verified. Withthe aid of plane water waves,diffraction phenomena of waves atdifferent obstacles (slit, edge, dou-ble-slit etc.) can be investigated. Inanother experiment the principle of“phased arrays antennas” can beanalysed by generating two circularwaves that interfere and by observ-ing the resulting interference onvarying the phase of one of thecircular waves.

3. By using the integrated vibrationgenerator as well as the externalvibration generator, generate twocircular waves and observe the in-terference. Vary the phase of theexternal wave generator with re-spect to the internal one and ob-serve the resulting interference tounderstand the principle of“phased arrays antennas”.

4. The external wave generator is con-nected to the water ripple tank andcircular waves are generated. Bymoving the external wave genera-tor the Doppler Effect is visualized.

Interference with the double slit.

Tasks:1. Generate two circular waves and

observe the resulting interfer-ence. Increase the number of cir-cular waves that interfere up toten by using all plugs of the“comb”. Recognize Huygens' Prin-ciple by investigating the result-ing interference for each case.

2. Generate plane water waves anduse a barrier to demonstrate inter-ference and diffraction at an edge.Then form a slit and observe inter-ference and diffraction behind theslit. Repeat this experiment for adouble-slit.

Ripple Tank with LED-light source , complete 11260.99 1

External vibration generator for ripple tank 11260.10 1

Connecting cable, 32 A, l = 50 cm, red 07361.01 1

Connecting cable, 32 A, l = 50 cm, blue 07361.04 1

Optional equipment for demonstration purposes in classes or lectures:

Demo set for Ripple Tank (USB-Camera, Fixing unit) 11260.20 1


or

Demo set with mirror for ripple tank 11260.30 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference and diffraction of water waves with the ripple tank P2133500

Mechanics Dynamics


� Diffraction of water waves� Interference of waves� Huygens' principle� Principle of

“phased arrays antennas”� Doppler effect

LEP_1_2 09.08.2007 11:35 Uhr Seite 52


Mechanics of Liquids and Gaseous Bodies Mechanics

Density of liquids 1.4.01-00

Principle:The density of water and glycerol isdetermined as a function of temper-ature using the Mohr balance.

Density of water as a function of temperature.

Tasks:The density of water and glycerol ismeasured in 1 to 2° steps over atemperature range from 0 to 20°C,then in larger steps up to 50°C.

Westphal/Mohr density balance 45016.00 1

Immersion thermostat TC10 08492.93 1

Accessory set for TC10 08492.01 1

Bath for thermostat, Makrolon 08487.02 1

Glycerol, 250 ml 30084.25 2

Water, distilled 5 l 31246.81 1

Sodium chloride, 500 g 30155.50 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDensity of liquids P2140100


� Hydrogen bond� H2O anomaly� Volume expansion� Melting� Evaporation� Mohr balance

LEP_1_2 09.08.2007 11:35 Uhr Seite 53

1.4.02-00 Surface of rotating liquids

Principle:A vessel containing liquid is rotatedabout an axis. The liquid surfaceforms a paraboloid of rotation, theparameters of which will be deter-mined as a function of the angularvelocity.

Location of the lowest point � c � of the liquid as a function of the angularvelocity.

Tasks:On the rotating liquid surface, thefollowing are determined:

1. the shape,

2. the location of the lowest point asa function of the angular velocity,

3. the curvature.


� Angular velocity� Centrifugal force� Rotary motion� Paraboloid of rotation� Equilibrium

Rotating liquid cell 02536.01 1



Motor with gearing, 12 VDC 11610.00 1






Methylene blue sol., alkal. 250 ml 31568.25 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedSurface of rotating liquids P2140200


Mechanics Mechanics of Liquids and Gaseous Bodies

LEP_1_2 09.08.2007 11:35 Uhr Seite 54



Viscosity of Newtonian and non-Newtonian liquids (rotary viscometer) 1.4.03-00

Principle:The viscosity of liquids can be deter-mined with a rotation viscometer, inwhich a motor with variable rotationspeed drives a cylinder immersed inthe liquid to be investigated with aspiral spring. The viscosity of the liq-uid generates a moment of rotationat the cylinder which can be meas-ured with the aid of the torsion ofthe spiral spring and read on a scale.

Temperature dependence of the viscosity of castor oil.

Tasks:1. Determine the gradient of the ro-

tational velocity as a function ofthe torsional shearing stress fortwo Newtonian liquids (glycerine,liquid paraffin).

2. Investigate the temperature de-pendence of the viscosity of Cas-tor oil and glycerine.

3. Determine the flow curve for anon-Newtonian liquid (chocolate).

Rotary viscosimeter 18221.93 1Support base -PASS- 02005.55 1Support rod, stainless steel 18/8, l = 500 mm 02032.00 1Right angle clamp 37697.00 1Magnetic stirrer MR 3001 K 35720.93 1Magnetic stirring rod, cylindrical, l = 30 mm 46299.02 1Separator for magnetic bars, PTFE 35680.03 1Beaker, DURAN®, short form, 600 ml 36015.00 3Beaker, DURAN®, tall form, 250 ml 36004.00 2Stirring rods, BORO 3.3, l = 200 mm, d = 5 mm 40485.03 1Digital thermometer, NiCr-Ni 07050.00 1Immersion probe NiCr-Ni,-50/1000°C 13615.03 1Glycerol, 250 ml 30084.25 2Liquid Paraffin, 250 ml 30180.25 1Castor oil, 250 ml 31799.27 2Acetone, chemical pure, 250 ml 30004.25 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedViscosity of Newtonian and non-Newtonianliquids (rotary viscometer) P2140300


� Shear stress� Velocity gradient� Internal friction� Viscosity� Plasticity

LEP_1_2 09.08.2007 11:35 Uhr Seite 55

1.4.04-00 Viscosity measurements with the falling ball viscometer

Principle:Due to internal friction among theirparticles, liquids and gases have dif-ferent viscosities. The viscosity, afunction of the substance’s structureand its temperature, can be experi-mentally determined, for example, bymeasuring the rate of fall of a ball ina tube filled with the liquid to be in-vestigated.

3. of methanol as a function of tem-perature.

From the temperature dependence ofthe viscosity, calculate the energybarriers for the displaceability ofwater and methanol.

Temperature dependence of the dynamic viscosity � of water (o) andmethanol (+), respectively.

Tasks:Measure the viscosity

1. of methanol-water mixtures ofvarious composition at a constanttemperature,

2. of water as a function of the tem-perature and


� Liquid� Newtonian liquid� Stokes law� Fluidity� Dynamic and kinematic

viscosity� Viscosity measurements



Falling ball viscosimeter 18220.00 1

Immersion thermostat C10 08492.93 1



Retort stand, h = 750 mm 37694.00 1

Right angle clamp 37697.00 1

Universal clamp with joint 37716.00 1

Pyknometer, 25 ml, calibrated 03023.00 1

Volumetric flasks with standard joint and PP stopper, BORO 3.3, 100 ml 36548.00 9

Beaker, DURAN®, tall form, 150 ml 36003.00 11

Beaker, DURAN®, short form, 250 ml 36013.00 1

Pasteur pipettes, l = 145 ml 36590.00 1

Rubber caps, 10 pcs 39275.03 1

Hose clip, d = 8-12 mm 40996.01 6

Rubber tubing, di = 6 mm, l = 1 m 39282.00 6


Laboratory balance, 120/240/620 g 48852.93 1

Wash bottle, plastic, 500 ml 33931.00 2

Methanol 500 ml 30142.50 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedViscosity measurements with the falling ballviscometer P2140400

LEP_1_2 09.08.2007 11:35 Uhr Seite 56



Surface tension by the ring method (Du Nouy method) 1.4.05-00

Principle:The force is measured on a ringshortly before a liquid film tearsusing a torsion meter. The surfacetension is calculated from the dia-meter of the ring and the tear-offforce.

Temperature dependency of surtace tension of olive oil.

Tasks:1. Determine the surface tension of

olive oil as a function of tempera-ture.

2. Determine the surface tension ofwater/methanol mixtures as func-tions of the mixture ratio.

Torsion dynamometer, 0.01 N 02416.00 1Surface tension measuring ring 17547.00 1Retort stand, 210 mm x 130 mm, h = 500 mm 37692.00 1Magnetic stirrer MR 3001 K 35720.93 1Support rod with hole, stainless steel, l = 50 cm, M10 thread 02022.20 1Magnetic stirring rod, cylindrical, l = 15 mm 46299.01 1Universal clamp 37718.00 2Right angle clamp 37697.00 2Right angle clamp -PASS- 02040.55 1Crystallizing dishes, BORO 3.3., 1000 ml 46245.00 2Crystallizing dishes, BORO 3.3., 560 ml 46244.00 2Laboratory thermometers, -10...+250°C 38065.00 1Silk thread on spool, l = 200 mm 02412.00 1Glass tube, AR-glass, straight, d = 8 mm, l = 150 mm, 10 pcs. 36701.64 1Glass stopcocks, 1 way, straight 36705.00 1Rubber tubing, di = 6 mm, l = 1 m 39282.00 2Volumetric pipettes, 10 ml 36578.00 1Volumetric pipettes, 20 ml 36579.00 1Safety pipettor Flip 36592.00 1Pipette dish 36589.00 1Graduated cylinder, BORO 3.3, 100 ml 36629.00 1Water jet pump, plastic 02728.00 1Ethyl alcohol, absolute, 500 ml 30008.50 1Olive oil, pure, 100 ml 30177.10 5Water, distilled 5 l 31246.81 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedSurface tension by the ring method(Du Nouy method) P2140500


� Surface energy� Interface� Surface tension� Adhesion� Critical point� Eötvös equation

LEP_1_2 09.08.2007 11:35 Uhr Seite 57

1.4.06-11 Surface tension by the pull-out method with Cobra3

Principle:The force exerted on a measuringring shortly before the liquid film istorn away is determined with a forcemeter. The surface tension is calcu-lated from the diameter of the ringand the tearing force.

Typical measurement values

Tasks:Determination of the surface tensionof water and other liquids.


� Surface energy� Surface tension� Surface adhesion� Bounding surface

Surface tension measuring ring 17547.00 1









Lab jack, 160 x 130 mm 02074.00 1

Petri dishes, d = 200 mm 64796.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedSurface tension by the pull-out methodwith Cobra3 P2140611



LEP_1_2 09.08.2007 11:35 Uhr Seite 58



Barometric height formula 1.4.07-00

Principle:Glass or steel balls are accelerated bymeans of a vibrating plate, andthereby attain different velocities(temperature model). The particledensity of the balls is measured as afunction of the height and the vibra-tional frequency of the plate.

Number of steel balls (m = 0.034 g), as a function of the height h, which passthrough the volume element �V in 30 seconds (vibrational frequency 50 Hz).

Tasks:Measurement of the particle densityas a function of:

1. the height, at fixed frequency

2. the vibrational frequency of theexciting plate, at fixed height.

Kinetic gas theory apparatus 09060.00 1

Variable transformer with rectifier 15 V~/12 V-, 5 A 13530.93 1










What you need:

Complete Equipment Set, Manual on CD-ROM includedBarometric height formula P2140700


� Kinetic gas theory� Pressure� Equation of state� Temperature� Gas constant

LEP_1_2 09.08.2007 11:35 Uhr Seite 59


1.4.08-00 Lift and drag (resistance to flow)

A) Objects of different cross-sectionand shape are placed in a laminarair stream. The drag is examinedas a function of the flow velocityand the geometry of the objects.

B) A rectangular plate or an aerofoilin a stream of air experiences abuoyant force (lift) and a resis-tance force (drag). These forces aredetermined in relation to area, rateof flow and angle of incidence.

Drag of an object as a function of its cross-sectional area A (q = 0.85 hPa).

B) Determination of the lift and thedrag of flat plates as a function of:

1. the plate area

2. the dynamic pressure

3. the angle of incidence (polar dia-gram)

4. Determination of the pressure dis-tribution over the aerofoil for var-ious angles of incidence.


� Resistance to pressure� Frictional resistance� Drag coefficient� Turbulent flow� Laminar flow� Reynolds number� Dynamic pressure� Bernoulli equation� Aerofoil� Induced resistance� Circulation� Angle of incidence� Polar diagram

Aerodynamic bodies, set of 14 02787.00 1

Aerofoil model 02788.00 1

Pitot tube, Prandtl type 03094.00 1

Precision manometer 03091.00 1

Holder with bearing points 02411.00 1

Double shaft holder 02780.00 1

Precision pulley 11201.02 1

Transparent spring balances, 0.2 N 03065.01 1

Vernier calipers, stainless steel 03010.00 1

Blower, mains voltage 220 V 02742.93 1

Power regulator 32288.93 1

Pipe probe 02705.00 1








Pointed rod 02302.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedLift and drag (resistance to flow) P2140800


Tasks:A) Determination of the drag as a

function of:

1. the cross-section of differentbodies,

2. the flow velocity,

3. determination of the drag coeffi-cients cw for objects of variousshape.

LEP_1_2 09.08.2007 11:35 Uhr Seite 60


Mechanical Vibration, Acoustics Mechanics

Vibration of strings 1.5.01-00

Principle:A tensioned metal string is made tovibrate. The vibrations of the stringare optically scanned, the vibrationprocess observed on the oscilloscopeand the dependence of the frequen-cy on the string tension and stringlength and the density of the mate-rial are investigated.

2. To measure the frequency for var-ious types and cross-sections ofstring, at a fixed tension andstring length.

Fundamental frequency f as a function of string length l at a given tension-ing force F = 30 N.

Tasks:1. To measure the frequency of a

string (e.g. constantan, 0.4 mmdia.) as a function of the tension-ing force and the length of thestring.

String tensioning device with rod 03431.01 1Nickel wire, d = 0.3 mm 06090.00 1Kanthal wire, 19.1 Ω/m, d = 0.3 mm, l = 100 m 06092.00 1Constantan wire, 6.9 Ω/m, d = 0.3 mm 06101.00 1Constantan wire, 0.98 Ω/m, d = 0.4 mm 06102.00 1Copper wire, d = 0.4 mm 06106.02 1Copper wire, d = 0.5 mm 06106.03 1Barrel base -PASS- 02006.55 1Bench clamp -PASS- 02010.00 3Support rod -PASS-, square, l = 250 mm 02025.55 3Right angle clamp -PASS- 02040.55 3Rod with hook 02051.00 1Sign holder 02066.00 2Fishing line on spool, d = 0,5 mm, l = 100 mm 02090.00 1Meter Scale, l = 1000 x 27 mm 03001.00 1Precision spring balances, 100.0 N 03060.04 1Striking hammer 03429.00 1Photoelement for optical base plate 08734.00 1Lamp socket E 10, G1 17049.00 1Filament lamps, 6 V/0.5 A 35673.03 1Distributor 06024.00 2Oscilloscope 30 MHz, 2 channels 11459.95 1LF amplifier, 220 V 13625.93 1Digital counter, 4 decades 13600.93 1Plug with push-on sleeve 07542.04 1Adapter, BNC socket - 4 mm plug 07542.20 1Adapter, BNC plug/4 mm socket 07542.26 2T type connector, BNC, socket, socket, plug 07542.21 1Adapter BNC socket/4 mm plug pair 07542.27 1Screened cable, BNC, l = 750 mm 07542.11 1Screened cable, BNC, l = 30 cm 07542.10 1Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 1Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedVibrations of strings P2150100


� Natural vibration� Mass-spring system� Harmonic sound intervals

LEP_1_2 09.08.2007 11:35 Uhr Seite 61

1.5.03-11 Velocity of sound in air with Cobra3

Principle:The speed of sound in air is deter-mined by measurements of soundtravel times.

Table 1

Tasks:Determination of the velocity ofsound in air.


� Linear relationship betweenthe propagation time ofsound and its respective path

� Longitudinal waves� Velocity of sound

What you need:

Complete Equipment Set, Manual on CD-ROM includedVelocity of sound in air with Cobra3 P2150311


Mechanics Mechanical Vibration, Acoustics

v /(m/s)

338.448

338.438

338.753

337.230

337.258



Software Cobra3, Timer/Counter 14511.61 1

Measuring microphone with amplifier 03543.00 1



Support 09906.00 1








LEP_1_2 09.08.2007 11:35 Uhr Seite 62



Acoustic Doppler effect 1.5.04-01/11

Principle:If a source of sound is in motion rel-ative to its medium of propagation,the frequency of the waves that areemitted is displaced due to theDoppler effect.

Table

Tasks:The frequency changes are measuredand analysed for different relativevelocities of source and observer.


� Propagation of sound waves� Doppler shift of frequency

Experiment P2150411 with Cobra3Experiment P2150401 with yt recorder

Power frequency generator, 1 MHz 13650.93 1

Yt recorder, 1 channel 11414.95 1

Meter Scale, l = 1000 x 27 mm 03001.00 1


Measuring microphone 03542.00 1 1

Flat cell battery, 9 V 07496.10 1 1

Loudspeaker/Sound head 03524.00 2 1

Car, motor driven 11061.00 1 1

Attachment for car 11061.02 1 1

Battery cell, 1.5 V, baby size, type C 07922.01 2 2

Barrel base -PASS- 02006.55 2 2

Stand tube 02060.00 1 1

Connecting cable, 4 mm plug, 32 A, yellow, l = 100 cm 07363.02 2 1



1 Track, l = 900 mm 11606.00 1 1

Connecting cord, 32 A, l = 1500 mm, red 07364.01 2





Function generator 13652.93 1

Plug with socket and crosshole, 2 pcs. 07206.01 1

Diaphragm, l = 100 mm 11202.03 1



Bosshead 02043.00 1

Support 09906.00 1

What you need:Movement toward Movement away fromthe sound source the sound source

v /m/s 0.162 0.157

v /m/s 0.159 0.156

v /m/s 0.158 0.157

v /m/s 0.159 0.156

Mean/m/s 0.160 0.157

Meanfmeasured/Hz 16199 16184

fcalculated/Hz 16199.6 16184.5

v




Double socket, pair red and black 07264.00 1



Complete Equipment Set, Manual on CD-ROM includedAcoustic Doppler effect P21504 01/11

Set-up of experiment P2150411 with Cobra3

LEP_1_2 09.08.2007 11:35 Uhr Seite 63


1.5.05-15 Chladni figures with FG-Module

Principle:To show the two-dimensional stand-ing waves on the surface of a squareor circular plate.

Tasks:A frequency generator is connectedto a sound head. The sound headdrives a Chaldni plate. White sand issprinkled randomly to cover the en-tire black surface of the plate. Drive the plate at a predeterminedharmonic frequency and the sandwill migrate into the nodal regions. A

Two dimensional oscillation of quadratic plates.

well defined standing wave patterncan be clearly seen in the first photo.The circular and square Chladniplates will create characteristic pat-terns. Adjust the oscillator slowly inthe 0.2 to 2 kHz frequency range andwatch for the pattern to emergewhen a harmonic is tuned.




Software Cobra3 PowerGraph 14525.61 1

Measuring module Function Generator 12111.00 1

LF amplifier, 220 V 13625.93 1

Loudspeaker/Sound head 03524.00 1

Sound pattern plates 03478.00 1

Support base, variable 02001.00 1

Bosshead 02043.00 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedChladni figures with FG-Module P2150515


� Wavelength� Stationary waves� Natural vibrations� Two-dimensional standing

waves


You can find more

experiments in Handbook

“Physics Experiments

with Cobra3”

Order No. 01310.02

LEP_1_2 09.08.2007 11:35 Uhr Seite 64



Velocity of sound using Kundt’s tube 1.5.06-01/15

Principle:A metal rod is made to vibrate longi-tudinally by rubbing it with a cloth.The gas column in a glass tube iscaused to vibrate naturally as aresult of resonance, through theradiation of sound from a discattached to the end of the rod.

The ratio of the velocities of sound inthe gas and in the vibration genera-tor is determined by measuring thewavelength.

Positions of the vibration nodes as a function of the number of nodes.

Tasks:1. To measure the wavelength of sta-

tionary waves using a steel or abrass rod as the vibration genera-tor. The longitudinal velocity ofsound in the material of the vibra-tion generator is determined,given the velocity of sound in air.

2. To measure the wavelength forCO2, and to determine the soundvelocity in CO2 from the ratios ofthe wavelengths in air determinedin 1. above.

Experiment P2150615 with FG-ModuleExp. P2150601 with vibration generator

Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 2Software Cobra3 PowerGraph 14525.61 1Measuring module Function Generator 12111.00 1LF amplifier, 220 V 13625.93 1Loudspeaker/Sound head 03524.00 1Support base, variable 02001.00 1Adapter BNC socket/4 mm plug pair 07542.27 1Screened cable, BNC, l = 750 mm 07542.11 1Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 1Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 1Glass tubes, AR-glass, d = 38 mm, l = 640 mm 03918.00 1 1Cork powder, 3 g 03477.00 1 1Universal clamp 37718.00 4 2Charging strip 03474.01 1Tuning piston 03474.02 1Vibration generator, brass 03476.01 1Vibration generator, steel 03476.02 1Lycopodium powder, 10 g 02715.00 1Laboratory thermometers, -10...+ 30°C 05949.00 1Bench clamp -PASS- 02010.00 4Meter Scale, l = 1000 x 27 mm 03001.00 1Pressure-reducing valves, CO2 / He 33481.00 1Steel cylinders, carbon dioxide, 10 l 41761.00 1Wrench for steel cylinders 40322.00 1Glass tube, AR-glass, straight, d = 8 mm, l = 80 mm, 10 pcs. 36701.65 1Rubber stopper, d = 38/31 mm, 1 hole, d = 7 mm 39260.01 1Rubber tubing, di = 6 mm, l = 1 m 39282.00 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedVelocity of sound using Kundt’s tube P21506 01/15


� Longitudinal waves� Sound velocity in gases and

solids� Frequency� Wavelength� Stationary waves� Natural vibrations

Set-up of experiment P2150615 with FG-Module

LEP_1_2 09.08.2007 11:36 Uhr Seite 65

1.5.07-01/15 Wavelengths and frequencies with a Quincke tube

Principle:If a sound wave of a particular fre-quency is divided into two coherentcomponents (like, for example, lightwaves in an interferometer experi-ment), and if the path of one of thecomponent waves is altered, it ispossible to calculate the wavelengthof the sound wave and its frequencyfrom the interference phenomenarecorded with a microphone.

Interference of sound waves in a Quincke tube. Sound amplitude as a func-tion of the displacement d.

Tasks:1. Record of the extension of a

Quincke tube for given frequen-cies in the range 2000 Hz to 6000Hz.

2. Calculation of the frequenciesfrom the wavelengths determined,comparison with the given fre-quencies.


� Transverse and longitudinalwaves

� Wavelength� Amplitude� Frequency� Phase shift� Interference� Velocity of sound in air� Loudness� Weber-Fechner law

Experiment P2150715 with FG-ModuleExperiment P2150701 with multimeter

Interference tube, Quincke type 03482.00 1 1

Measuring microphone 03542.00 1




Loudspeaker/Sound head 03524.00 1 1

Vernier calipers, stainless steel 03010.00 1 1



Support base -PASS- 02005.55 1 1

Support rod -PASS-, square, l = 630 mm 02027.55 2 2

Right angle clamp -PASS- 02040.55 5 5






Connection box 06030.23 1

Carbon resistor 10 Ω, 1W, G1 39104.01 1


Support 09906.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedWavelengths and frequencies with a Quincke tube P2150701/15




LEP_1_2 09.08.2007 11:36 Uhr Seite 66



Resonance frequencies of Helmholtz resonators with Cobra3 1.5.08-11

Principle:Acoustic cavity resonators posses acharacteristic frequency which is de-termined by their geometrical form.In this case the resonator is excitedto vibrations in its resonance fre-quency by background noise.

Time signal, spectrum and parameter settings for measurements on the empty1000 ml round-bottomed flask.

Tasks:Determination of different resonancefrequencies of a resonator dependingon the volume.



Software Cobra3 Fourier Analysis 14514.61 1



Glass tubes, AR-glass, d = 12 mm, l = 300 mm 45126.01 1



Universal clamp 37718.00 2

Bosshead 02043.00 2


Long-neck round-bottom flask, 1000 ml 36050.00 1

Long-neck round-bottom flask, 1000 ml 36046.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedResonance frequencies of Helmholtz resonators with Cobra3 P2150811


� Cavity resonator� Resonance frequency� Acoustic resonant circuit

LEP_1_2 09.08.2007 11:36 Uhr Seite 67

1.5.09-11 Interference of acoustic waves, stationary waves and diffraction at a slot with PC interface

Principle:– Two acoustic sources emit waves

of the same frequency and if theirdistance is a multiple of the wave-length, an interference structurebecomes apparent in the spacewhere the waves are superim-posed.

– An acoustic wave impinges per-pendicularly onto a reflector, theincident and the reflected waveare superimposed to a stationarywave. In case of reflection, a pres-sure antinode will always occur atthe point of reflection.

– An acoustic wave impinges on asufficiently narrow slot, it is dif-fracted into the geometrical shad-ow spaces. The diffraction and theinterference pattern occurringbehind the slot can be explainedby means of the Huygens-Fresnelprinciple and confirm the wavecharacteristics of sound.

Measurement example, stationary waves.

Tasks:1. To measure the interference of

acoustic waves.

2. To analyze the reflection of acous-tic waves – stationary waves.

3. To measure the diffraction at aslot of acoustic waves.


� Interference� Reflection� Diffraction� Acoustic waves� Stationary waves� Huygens-Fresnel principle� Use of an interface

Loudspeaker/Sound head 03524.00 2

Measuring microphone 03542.00 1


Screen, metal, 300 mm x 300 mm 08062.00 2







Meter Scale, l = 1000 x 27 mm 03001.00 1


Weight holder, 1 g, silver bronzing 02407.00 1












What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference of acoustic waves, stationary wavesand diffraction at a slot with PC interface P2150911



LEP_1_2 09.08.2007 11:36 Uhr Seite 68



Optical determination of velocity of sound in liquids 1.5.10-00

Principle:A stationary ultrasonic wave in aglass cell full of liquid is traversed bya divergent beam of light. The soundwavelength can be determined fromthe central projection of the soundfield on the basis of the refractiveindex which canges with the soundpressure.

Image of a screen.

Ultrasonic generator 13920.99 1

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1

Glass cell, 150 x 55 x 100 mm 03504.00 1

Lens holder 08012.00 1

Lens, mounted, f = +20 mm 08018.01 1


Optical profile bench, l = 1000 mm 08282.00 1

Base for optical profile bench, adjustable 08284.00 2

Slide mount for optical profil bench, h = 80 mm 08286.02 1


Swinging arm 08256.00 1

Table top on rod 08060.00 1

Laboratory thermometers, -10...+ 30°C 05949.00 1




Glycerol, 250 ml 30084.25 3


What you need:

Complete Equipment Set, Manual on CD-ROM includedOptical determination of velocityof sound in liquids P2151000


� Ultrasonics� Sound velocity� Frequency� Wavelength� Sound pressure� Stationary waves

Tasks:To determine the wavelength ofsound in liquids, and from this calu-cate the sound velocity, from thestructure of the centrally projectedimage.

LEP_1_2 09.08.2007 11:36 Uhr Seite 69

1.5.11-00 Phase and group velocity of ultrasonics in liquids

Principle:The sound waves transmitted to aliquid by the ultrasonic generator arepicked up by a piezoelectric ultra-sonic pick-up and the signal fromtransmitter and receiver comparedon an oscilloscope.

The wavelength is determined andthe phase velocity calculated fromthe relative phase position of thesignals. The group velocity is deter-mined from measurements of thesound pulse delay time.

2.1. To determine the oscilloscope’scoefficient of sweep with the aidof the ultrasonic frequency.

2.2. With the generator in the pulsedmode, to record the delay timeof the sound pulses as a functionof the distance between a gen-erator and the pick-up, and todetermine the group velocity.

Detector displacement �l as a function of the number n of wavelengths cov-ered, for water, glycerol and sodium chloride solution (temperature � = 25°C).

Tasks:The signals from the ultrasonic gen-erator and the ultrasonic pick-up arerecorded on the oscilloscope.

1. To measure the relative phaseposition of the signal from theultrasonic pick-up as a function ofits distance from the ultrasonicgenerator (which is in the sinemode), and to determine theultrasonic wavelength and thephase velocity when the frequen-cy is known.


� Longitudinal waves� Velocity of sound in liquids� Wavelength� Frequency� Piezoelectric effect� Piezoelectric ultrasonics

transformer

Ultrasonic pickup 13920.00 1


Glass cell, 150 x 55 x 100 mm 03504.00 1

Insulating support 07924.00 1





Table top on rod 08060.00 1





Oscilloscope 30 MHz, 2 channels 11459.95 1




Laboratory thermometers, -10...+ 30°C 05949.00 1

Glycerol, 250 ml 30084.25 3



What you need:

Complete Equipment Set, Manual on CD-ROM includedPhase and group velocity of ultrasonicsin liquids P2151100



LEP_1_2 09.08.2007 11:36 Uhr Seite 70



Temperature dependence of the Velocity of sound in liquids 1.5.12-00

Principle:Sound waves are radiated into a liq-uid by an ultrasonic transmitter anddetected with a piezoelectric trans-ducer. The wavelength of the soundis found by comparing the phase ofthe detector signal for differentsound paths and, when the frequen-cy is known, the velocity of sound asa function of the temperature of theliquid is determined.

termined when the ultrasonic fre-quency is known. The measurementis made for water and glycerol as thetemperatures of the liquids arechanged step-by-step.

Velocity of sound in water as a function of the temperature.

Tasks:The wavelength is found from thephase position of the sound pickupsignal relative to the generator sig-nal as a function of the sound pathand the velocity of the sound is de-

Ultrasonic pickup 13920.00 1


Sliding device, horizontal 08713.00 1









Laboratory thermometers, -10...+100°C 38056.00 1







Glycerol, 250 ml 30084.25 1



Slide mount 08286.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedTemperature dependence of the Velocityof sound in liquids P2151200


� Wavelength� Frequency� Velocity of sound in liquids� Compressibility� Density� Ultrasonics� Piezoelectric effect� Piezoelectric ultrasonic

transducer

LEP_1_2 09.08.2007 11:36 Uhr Seite 71


1.5.13-00 Stationary ultrasonic waves, determination of wavelength

Principle:An ultrasonic wave is subjected tosurface reflection from a metal plate.The reflected wave superimposes onthe incident wave, coincident inphase and amplitude, to form astanding wave. The intensity of thiswave along the direction of propaga-tion is measured using a movable ul-trasonic receiver.

The change in the sound pressure intensity in the direction of propagation asa function of the distance.

Tasks:1. Determine the intensity of a

standing ultrasonic wave by mov-ing an ultrasonic receiver alongthe direction of propagation.

2. Plot a graph of the measured val-ues as a function of the distance.

3. Determine the wavelength of theultrasonic wave.

Ultrasound operation unit 13900.00 1


Ultrasonic transmitter 13901.00 1

Ultrasonic receiver on stem 13902.00 1











What you need:

Complete Equipment Set, Manual on CD-ROM includedStationary ultrasonic waves, determinationof wavelength P2151300



� Longitudinal waves � Superposition of waves� Reflection of longitudinal

waves� Stationary longitudinal waves

LEP_1_2 09.08.2007 11:36 Uhr Seite 72


Absorption of ultrasonic in air 1.5.14-00


Principle:Sound needs a material medium withwhich it can enter into reciprocal ac-tion for its propagation, whereby aloss of energy occurs. The amplitude,and so also the intensity, decreasesalong the propagation path.

The change in sound pressure intensity as a function of the distance from thesource of sound.

Tasks:1. Move an ultrasonic receiver along

the direction of propagation of asound wave to measure the soundintensity as a function of the dis-tance from the source of thesound.

2. Plot linear and logarithmic graphsof the values of the sound intensi-ty as a function of the distance.

3. Confirm the law of absorption anddetermine the absorption coeffi-cient.

4. Verify that the emitted wave is aspherical wave near to the trans-mitter.


� Longitudinal waves� Plane waves� Spherical waves� Propagation of sound waves� Sound pressure� Alternating sound pressure� Sound intensity� Absorption coefficient of

ultrasonic waves� Law of absorption











What you need:

Complete Equipment Set, Manual on CD-ROM includedAbsorption of ultrasonic in air P2151400

LEP_1_2 09.08.2007 11:36 Uhr Seite 73


1.5.15-15 Ultrasonic diffraction at different single and double slit systems

Principle:A plane ultrasonic wave is subjectedto diffraction at single slits of vari-ous widths and at various doubleslits. The intensity of the diffractedand interfering partial waves are au-tomatically recorded using a motor-driven, swivel ultrasound detectorand a PC.

The angular distribution of the intensity of a plane ultrasonic wave diffract-ed at a slit.

Tasks:1. Record the intensity of an ultra-

sonic wave diffracted by variousslits and double slits as a functionof diffraction angle.

2. Determine the angular positionsof the maximum and minimumvalues and compare them with thetheoretical results.

Goniometer with reflecting mirror 13903.00 1

Goniometer Operation Unit 13903.99 1





Object holder for goniometer 13904.00 1

Diffraction objects for ultrasonic 13905.00 1





Software Goniometer 14523.61 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic diffraction at different singleand double slit systems P2151515



� Longitudinal waves � Huygens’ principle� Interference� Fraunhofer and Fresnel

diffraction

LEP_1_2 09.08.2007 11:36 Uhr Seite 74


Ultrasonic diffraction at different multiple slit systems 1.5.16-15


Principle:An ultrasonic plane wave is subject-ed to diffraction at various multipleslits. The intensity of the diffractedand interfering partial waves are au-tomatically recorded using a motor-driven, swivel ultrasound detectorand a PC.

The angular distribution of the intensity of a plane ultrasonic wave diffract-ed by a fourfold slit.

Tasks:1. Determine the angular distribu-

tion of a plane ultrasonic wavediffracted by various multiple slits.

2. Determine the angular positionsof the maximum and mininumvalues and compare them with thetheoretical values.


� Longitudinal waves � Huygens’ principle� Interference� Fraunhofer and Fresnel

diffraction








Diffraction objects for ultrasonic 13905.00 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic diffraction at different multipleslit systems P2151615

LEP_1_2 09.08.2007 11:36 Uhr Seite 75


1.5.17-15 Diffraction of ultrasonic waves at a pin hole and a circular obstacle

Principle:An ultrasonic plane wave is subject-ed to diffraction by a pin-hole obsta-cle and a complementary circularobstacle. The intensity distribution ofthe diffracted and interfering partialwaves are automatically recordedusing a motor-driven, swivel ultra-sound detector and a PC.

The angular distribution of the intensity of a plane ultrasonic wave diffract-ed by a pin-hole obstacle.


tion of an ultrasonic wavediffracted by a pin-hole and circu-lar obstacle.

2. Compare the angular positions ofthe minimum intensities with thetheoretical values.








Pin hole and circular obstacle for ultrasonic 13906.00 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction of ultrasonic waves at a pin holeand a circular obstacle P2151715



� Longitudinal waves� Huygens’ principle� Interference� Fraunhofer and Fresnel

diffraction� Fresnel’s zone construction� Poisson’s spot� Babinet’s theorem� Bessel function

LEP_1_2 09.08.2007 11:36 Uhr Seite 76


Ultrasonic diffraction at Fresnel lenses / Fresnel’s zone contruction 1.5.18-00


Principle:An ultrasonic plane wave strikes aFresnel zone plate. The ultrasonic in-tensity is determined as a function ofthe distance behind the plate, usingan ultrasonic detector that can bemoved in the direction of the zoneplate axis.

Graph of the intensity of the ultrasound as a function of the distance from aFresnel zone plate( curve a ); curve b without zone plate.

Tasks:1. Determine and plot graphs of the

intensity of the ultrasonic behinddifferent Fresnel zone plates as afunction of the distance behindthe plates.

2. Carry out the same measurementseries without a plate.

3. Determine the image width ateach distance of the transmitterfrom the zone plate and comparethe values obtained with thosetheoretically expected.


� Longitudinal waves� Huygens’ principle� Interference� Fraunhofer and Fresnel

diffraction� Fresnel’s zone construction� Zone plates





Fresnel zone plates for ultrasonic 13907.00 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic diffraction at Fresnel lenses /Fresnel’s zone contruction P2151800

LEP_1_2 09.08.2007 11:36 Uhr Seite 77


1.5.19-15 Interference of two identical ultrasonic transmitters

Principle:Ultrasonic waves of the same fre-quence, amplitude and direction ofpropagation are generated by twosources positioned parallel to eachother. The sources can vibrate bothin-phase and out-of phase. The an-gular distribution of the intensity ofthe waves, which interfere with eachother, is automatically recordedusing a motor-driven ultrasonic de-tector and a PC.

Angular distribution of the intensity of two interfering ultrasonic waves hav-ing the same phase, amplitude, frequency and direction of propagation.


tion of the sound pressure of twoultrasonic transmitters vibratingin-phase.

2. Determine the angular positionsof the interference minima andcompare the values found withthose theoretically expected.

3. Repeat the measurements withthe two ultrasonic transmitters vi-brating out-of-phase.

4. Repeat the first measurement andadditionally determine with theangular distribution of the soundpressure of each single transmitter.














What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference of two indentical ultrasonictransmitters P2151915



� Longitudinal waves� Sound pressure� Huygens’ principle� Interference� Fraunhofer and Fresnel

diffraction

LEP_1_2 09.08.2007 11:36 Uhr Seite 78


Interference of ultrasonic waves by a Lloyd mirror 1.5.20-00


Principle:A partial packet of radiation passesdirectly from a fixed ultrasonictransmitter to a fixed ultrasonic re-ceiver. A further partial packet hitsagainst a metal screen that is posi-tioned parallel to the connecting linebetween the transmitter and receiv-er, and is reflected in the direction ofthe receiver. The two packets of radi-ation interfere with each other atthe receiver. When the reflector ismoved parallel to itself, the differ-ence in the path lengths of the twopackets changes. According to thisdifference, either constructive or de-structive interference occurs.

The received signal as a function of the reflector distance d.

Tasks:1. The sliding device is to be used to

move the reflector screen posi-tioned parallel to the connectingline between the transmitter andreceiver parallel to itself in stepsof d = (0.5-1) mm. The reflectorvoltage U is to be recorded at eachstep.

2. The d values of the various maxi-ma and minima are to be deter-mined from the U = U(d) graphand compared with the theoreti-cally expected values.


� Longitudinal waves� Superposition of waves� Reflection of longitudinal

waves� Interference
















What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference of ultrasonic waves by a Lloyd mirror P2152000

LEP_1_2 09.08.2007 11:36 Uhr Seite 79


1.5.21-15 Determination of the velocity of sound (sonar principle)

Principle:An ultrasonic transmitter emitssound pulses onto a reflector, fromwhich recording of them by a receiv-er shows a time delay. The velocity ofsound is calculated from the pathlength and transmission time of thesound pulses.

Measured time between the transmitted and the received reflected ultrasonicwaves.

Tasks:1. Determine transmission times for

different distances apart of thetransmitter and the receiver.

2. Plot a graph of the path lengths ofthe sound pulses against theirtransmission time.

3. Determine the velocity of soundfrom the graph.










Meter Scale, l = 1000 x 27 mm 03001.00 1



Software Cobra3 Universal recorder 14504.61 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedDetermination of the velocity of sound(sonar principle) P2152115



� Longitudinal waves� Sound pressure� Phase- and group velocity� Sonar principle

LEP_1_2 09.08.2007 11:36 Uhr Seite 80


Ultrasonic Michelson-Interferometer 1.5.22-00


Principle:A “semi-permeable“ membrane di-vides an ultrasonic wave into twopartial packets which travel at rightangles to each other. They are subse-quently reflected at different hardmetal reflectors, one of which is fixedin position, and the other of whichcan be displaced in the direction ofthe beam, before being reunited.Shifting the displaceable reflectorchanges the path length of the corre-sponding packet, so that superposi-tioning of the reunited partial pack-ets gives maxima and minima of thealternating sound pressure accordingto the differenc in the distance trav-elled. The wavelength of the ultra-sound can be determined from these.

Intensity of the alternating sound pressure as a function of the displacement�d of reflector screen Sc2.

Tasks:1. Determine the intensity of the

alternating sound pressure in de-pendence on the displacement ofone of the reflectors.

2. Calculate the wavelength of theultrasound from the measurementcurve.


� Longitudinal waves� Reflection of longitudinal

waves� Superposition of waves� Interference� Interferometer





Multi range meter, analogue 07028.01 1







Screen, translucent, 250 mm x 250 mm 08064.00 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic Michelson-Interferometer P2152200

LEP_1_2 09.08.2007 11:36 Uhr Seite 81


1.5.23-00 Ultrasonic diffraction by a straight edge

Principle:An ultrasonic wave hits a straightedge which limits the wave field toone side. According to Huygens’principle, the edge is a point sourcefor secondary waves, and these pen-etrate also into the shaded area ofthe edge. In the transmission range,secondary waves interfere with theprimary waves, so that a successionof maxima and minima of the alter-nating sound pressure are createdtransverse to the edge.

Diffraction at an edge: Course of intensity of the alternating sound pressureas function of position coordinate x.

Tasks:1. Determine the intensity distribu-

tion of an ultrasonic wavediffracted at a straight edge as afunction of the transverse dis-tance from the edge.

2. Compare the positions of themaxima and minima found in theexperiment to those theoreticallyexpected.

3. Repeat the measurement of theintensity distribution of the ultra-sonic wave without the straightedge.


















What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic diffraction by a straight edge P2152300



� Longitudinal waves� Superposition of waves� Huygens’ principle� Interference� Fraunhofer and Fresnel

diffraction� Fresnel zones� Fresnel integrals� Cornu’s spiral

LEP_1_2 09.08.2007 11:36 Uhr Seite 82


Ultrasonic Doppler effect 1.5.24-15


Principle:If a source of sound is in motion rel-ative to its medium of propagation,the frequency of the waves that areemitted is displaced due to theDoppler effect.

Doppler shift of frequency.

Tasks:The frequency changes are measuredand analysed for different relativevelocities of source and observer.


� Propagation of sound waves� Superimposition of sound

waves� Doppler shift of frequency� Longitudinal waves





Car, motor driven 11061.00 1

Attachment for car 11061.02 1

Battery cell, 1.5 V, baby size, type C 07922.01 2



Connecting cord, 32 A, l = 1000 mm, red 07363.01 1

Connecting cable, 32 A, l = 1000 mm, yellow 07363.02 1

Connecting cable, 32 A, l = 1000 mm, blue 07363.04 1

Connecting cable, 32 A, l = 100 mm, yellow 07359.02 1



Track, l = 900 mm 11606.00 1



Data cable, plug/socket, 9 pole 14602.00 1


Double socket, 1 pair, red and black 07264.00 1


Screen with plug, l = 100 mm 11202.03 1

Support rod, stainless steel, l = 600 mm 02037.00 1


Bosshead 02043.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic Doppler effect P2152415

LEP_1_2 09.08.2007 11:36 Uhr Seite 83


Physics Experiments – Linear Motion

Newton’s second law with Cobra3 and demonstration track.

Mechanics Handbooks

In the experimental literature “Linear Motion” you will find detailed descriptions ofexperiments regarding the following concepts:● Uniform acceleration and deceleration

● Momentum (elastic and inelastic collision)

● Newton’s laws

● Potential and kinetic energy

● Grade resistance/inclined plane

Almost all experiments can be performed either with the 2 m long air track 11202.17 orwith the 1.5 m long demonstration track 11305.00. For the measurements and data record-ing you can use the Cobra3 interface 12150.00, the 4-4 Timer 13605.99 or the 6-decadedigital counter 13603.93.

Physics Experiments – Linear Motion • No. 16001.02 • 15 Experiments described

1.1 P1198511The linear uniform motion

2.1 P1198615Uniformly accelerated motion with an accelerating mass

2.2 P1198702Uniformly accelerated motion with a jet glider

2.3 P1198805Uniformly accelerated motion withan inclined track

2.4 P1198906Uniformly decelerated motion

2.5 P1199000The free fall

3.1 P1199115Law of inertia (Newton's 1st law)

3.2 P1199201Fundamental law of dynamics(Newton's 2nd Law)

3.3 P1199306Law of reciprocal actions(Newton's 3rd Law)

3.4 P1199405Equivalence of inert mass and heavy mass

3.5 P1198115Velocity-independent and velocity-dependent friction with Demo-Trackand Cobra3

3.6 P1198215The inertial force F = m · a with Demo-Track and Cobra3

4.1 P1199502Impulse and momentum

4.2 P1199605Conservation of momentum in elastic collisions

4.3 P1199711Conservation of momentum ininelastic collisions

4.4 P1199801Conservation of momentum in multiple elastic collisions

4.5 P1199902Conservation of momentum in multiple inelastic collisions

Conservation of momentum in multiple inelastic collisions with 4-4 Timer andair track.

LEP_1_2 09.08.2007 11:36 Uhr Seite 84


Handbooks Mechanics

1 Forces

MT 1.1 (12516)Mass and weight

MT 1.2 (12517)Extension of a rubber band and helical spring

MT 1.3 (12518)Hooke’s law

MT 1.4 (12519)Making and calibrating adynamometer

MT 1.5 (12520)Bending a leaf spring

MT 1.6 (12521)Force and counterforce

MT 1.7 (12522)Composition of forces having the same line of application

MT 1.8 (12523)Composition of non-parallel forces

MT 1.9 (12524)Resolution of a force into two non-parallel forces

MT 1.10 (12525)Resolution of forces on an inclinedplane

MT 1.11 (12526)Resolution of forces on a crane

MT 1.12 (12527)Restoring force on a displaced pendulum

MT 1.13 (12528)Determination of the centre ofgravity of an irregular plate

MT 1.14 (12529)Frictional force

MT 1.15 (12530)Determination of the coefficient offriction on an inclined plane

2 Simple machines

MT 2.1 (12531)Double-sided lever

MT 2.2 (12532)One-sided lever

MT 2.3 (12533)Double-sided lever and more thantwo forces

MT 2.4 (12534)Reaction at the supports

MT 2.5 (12535)Moment of rotation (torque)

MT 2.6 (12536)Beam balance

MT 2.7 (12537)Sliding weight balance

MT 2.8 (12538)Fixed pulley

MT 2.9 (12539)Free pulley

MT 2.10 (12540)Block and tackle

MT 2.11 (12541)Step wheel

MT 2.12 (12542)Toothed-gearing

MT 2.13 (12543)Belt drives

3 Oscillations

MT 3.1 (12544)Thread pendulum

MT 3.2 (12545)Spring pendulum

MT 3.3 (12546)Physical pendulum(reversible pendulum)

DEMONSTRATION EXPERIMENTS

PHYSICS


0115

2.02

Winfried Rössler

Georg Schollmeyer

The use of the demonstration board for physics offers the following advantages for the lecturer:● Minimal preparation time

● Lucid and simple set-up

● Labelling of the experiment directly on the board

● Magnet-held arrows, linear and angular scales

● Stable storage box

● Both sides of board can be used for mechanics and optics

● Galvanised sheet steel board in aluminium profile frame

● Mechanics side: lacquered

● Optic side: white foil with lined grid

Physics Demonstration Experiments – Magnet Board Mechanics 1

Physics Demonstration Experiments – Magnet Board Mechanics 1 • No. 01152.02 • 31 described ExperimentsPlease ask for a complete equipment list Ref. No. 21701

Fixed pulley (MT 2.8)

Resolution of forces on an inclined plane (MT 1.10)

LEP_1_2 09.08.2007 11:36 Uhr Seite 85


Mechanics Handbooks

4 Movement

MT 4.1 (12960)Uniform rectilinear movement

MT 4.2 (12961)Uniform accelerated rectilinearmovement

MT 4.3 (12962)Horizontal and sloping trajectories

MT 4.4 (12963)Newton’s basic principle

5 Forms of Mechanical Energy

MT 5.1 (12964)Energy transformation duringupward and downward runs

MT 5.2 (12965)Kinetic energy

MT 5.3 (12966)Energy of refraction

6 Mechanics of Fluids and Gases

MT 6.1 (12967)U-tube manometer

MT 6.2 (12968)Hydrostatic pressure

MT 5.3 (12969)Communicating vessels

MT 6.4 (12970)Hydraulic press

MT 6.5 (12971)Artesian well

MT 6.6 (12972)Archimedes principle

MT 6.7 (12973)Density determination by measuringbuoyancy

MT 6.8 (12974)Discharge velocity of a vessel

MT 6.9 (12975)Pressure in flowing fluids

MT 6.10 (12976)Pressure in gases

MT 6.11 (12977)Boyle and Mariotte’s law


PHYSICS


0115

2.02

Winfried Rössler

Georg Schollmeyer

The use of the demonstration board for physics offers the following advantagesfor the lecturer:● Minimal preparation time

● Lucid and simple set-up

● Labelling of the experiment directly on the board

● Magnet-held arrows, linear and angular scales

● Stable storage box

● Both sides of board can be used for mechanics and optics

● Galvanised sheet steel board in aluminium profile frame

● Mechanics side: lacquered

● Optic side: white foil with lined grid

Physics Demonstration Experiments – Magnet Board Mechanics 2

Horizontal and sloping trajectories (MT 4.3)

Energy transformation during upward and downward runs (MT 5.1)

Physics Demonstration Experiments – Magnet Board Mechanics 2 • No. 01153.02 • 18 described ExperimentsPlease ask for a complete equipment list Ref. No. 21702

LEP_1_2 09.08.2007 11:36 Uhr Seite 86

2Optics

LEP_2 09.08.2007 11:42 Uhr Seite 87


Contents

2.1 Geometrical Optics

2.1.01-00 Measuring the velocity of light


2.1.03-00 Dispersion and resolving power of the prism and grating spectroscope

2.2 Interference


2.2.02-00 Newton’s rings


2.2.04-00 Fresnel’s zone construction / zone plate


2.2.06-00 Coherence and width of spectral lines with Michelson interferometer


2.3 Diffraction

2.3.01-00 Diffraction at a slit and Heisenberg’s uncertainty principle


2.3.03-00 Intensity of diffractions due to pin hole diaphragms and circular obstacles

2.3.04-00 Diffraction intensity of multiple slits and grids

2.3.05-00 Determination of the diffraction intensity at slit and double slit systems


2.4 Photometry

2.4.02-01 Photometric law of distance


2.4.04-00 Lambert’s law

Optics

2.5 Polarisation

2.5.01-00 Polarisation by quarterwave plates

2.5.02-00 Polarimetry


2.5.04-00 Malus’ law

2.6 Applied Optics


2.6.02-00 Kerr effect


2.6.04-00 CO2-laser


2.6.07-01 Helium Neon Laser


2.6.09-00 Nd-YAG laser


2.6.11-00 Fourier optics – 2f Arrangement


2.7 Handbooks

Advanced Optics and Laser Physics


2LEP_2 09.08.2007 11:42 Uhr Seite 88


Measuring the velocity of light 2.1.01-00

Geometrical Optics Optics

Principle:The intensity of the light is modulat-ed and the phase relationship of thetransmitter and receiver signal com-pared. The velocity of light is calcu-lated from the relationship betweenthe changes in the phase and thelight path.

Measuring the velocity of light in other media.

Tasks:1. To determine the velocity of light

in air.

2. To determine the velocity of lightin water and synthetic resin andto calculate the refractive indices.


� Refractive index� Wavelength� Frequency� Phase� Modulation� Electric field constant� Magnetic field constant

Light velocity measuring apparatus 11224.93 1



Block, synthetic resin 06870.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMeasuring the velocity of light P2210100

LEP_2 09.08.2007 11:42 Uhr Seite 89



Principle:The focal lengths of unknown lensesare determined by measuring thedistances of image and object and byBessel’s method. Simple opticalinstruments are then constructedwith these lenses.

Path of a ray in Galileo telescope.

Tasks:1. To determine the focal length of

two unknown convex lenses bymeasuring the distances of imageand object.

2. To determine the focal length of aconvex lens and of a combinationof a convex and a concave lensusing Bessel’s method.

3. To construct the following opticalinstruments:1. Slide projector; image scale to

be determined2. Microscope; magnification to

be determined3. Kepler-type telescope4. Galileo’s telescope

(opera glasses).

Lens, mounted, f = +20 mm 08018.01 1

Lens, mounted, f = +50 mm 08020.01 1

Lens, mounted, f = +100 mm 08021.01 1

Lens, mounted, f = +300 mm 08023.01 1

Lens, mounted, f = -50 mm 08026.01 1

Lens, mounted, f = -200 mm 08028.01 1


Screen with arrow slit 08133.01 1

Ground glass screen, 50 mm d = 50 mm 08136.01 1

Double condenser, f = 60 mm 08137.00 1

Object micrometer 1mm i.100 parts 62171.19 1

Ctenocephalus, msl 87337.10 1

Slide -Emperor Maximilian- 82140.00 1





Diaphragm holder for optical base plate 08040.00 2


Condenser holder 08015.00 1


Experimenting lamp 5, with stem 11601.10 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of lenses and optical instruments P2210200

Optics Geometrical Optics


� Law of lenses� Magnification� Focal length� Object distance� Telescope� Microscope� Path of a ray� Convex lens� Concave lens� Real image� Virtual image

LEP_2 09.08.2007 11:42 Uhr Seite 90


Dispersion and resolving power of the prism and grating spectroscope 2.1.03-00

Geometrical Optics Optics

Principle:The refractive indices of liquids,crown glass and flint glass are deter-mined as a function of the wave-length by refraction of light throughthe prism at minimum deviation. Theresolving power of the glass prisms isdetermined from the dispersioncurve.

Tasks:1. To adjust the spectrometer-gonio-

meter.

2. To determine the refractive indexof various liquids in a hollow prism.

3. To determine the refractive indexof various glass prism.

4. To determine the wavelengths ofthe mercury spectral lines.

5. To demonstrate the relationshipbetween refractive index andwavelength (dispersion curve).

6. To calculate the resolving powerof the glass prisms from the slopeof the dispersion curves.

Dispersion curves of various substances.

7. Determination of the grating con-stant of a Rowland grating basedon the diffraction angle (up to thethird order) of the high intensityspectral lines of mercury.

8. Determination of the angular dis-persion of a grating.

9. Determination of the resolvingpower required to separate thedifferent Hg-Lines. Comparisonwith theory.


� Maxwell relationship� Dispersion� Polarizability� Refractive index� Prism� Rowland grating� Spectrometer-goniometer

Spectrometer/goniometer with verniers 35635.02 1

Lamp holder, pico 9, for spectral lamps 08119.00 1

Spectral lamp Hg 100, pico 9 base 08120.14 1

Power supply for spectral lamps 13662.97 1

Prism, 60°, Crownglass, h = 30 mm 08231.00 1

Hollow prism 60°, l = 60 mm, h = 60 mm 08240.00 1

Diffraction grating, 4 lines/mm 08532.00 1


Diffraction grating,10 lines/mm 08540.00 1










Glycerol, 250 ml 30084.25 1

Methanol 500 ml 30142.50 1

Cyclohexane for synthesis, 100 ml 31236.10 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDispersion and resolving power of the prism and grating spectroscope P2210300

LEP_2 09.08.2007 11:42 Uhr Seite 91


Principle:By dividing up the wave-front of abeam of light at the Fresnel mirrorand the Fresnel biprism, interferenceis produced. The wavelength is de-termined from the interference pat-terns.

Geometrical arrangement, using the Fresnel mirror.

Tasks:Determination of the wavelength oflight by interference

1. with Fresnel mirror,

2. with Fresnel biprism.


� Wavelength� Phase� Fresnel biprism� Fresnel mirror� Virtual light source

Fresnel biprisms 08556.00 1

Prism table with holder 08254.00 1

Fresnel mirror 08560.00 1

Lens, mounted, f = +20 mm 08018.01 1

Lens, mounted, f = +300 mm, achromatic 08025.01 1







Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference of light P2220100


Optics Interference

LEP_2 09.08.2007 11:42 Uhr Seite 92


Interference Optics

Newton’s rings 2.2.02-00

Principle:In a Newton’s rings apparatus,monochromatic light interferes inthe thin film of air between theslightly convex lens and a plane glassplate. The wavelengths are deter-mined from the radii of the interfer-ence rings.

Radius of the interference rings as a function of the order number for variouswavelengths.

Tasks:Using the Newton’s rings apparatus,to measure the diameter of the ringsat different wavelengths and:

1. to determine the wavelengths fora given radius of curvature of thelens

2. to determine the radius of curva-ture at given wavelengths.

Newton rings apparatus 08550.00 1

Lens, mounted, f = + 50 mm 08020.01 1

Interference filters, set of 3 08461.00 1


Mercury vapour high pressure lamp, 50 W 08144.00 1

Power supply 230V/50 Hz for 50 W Hg-lamp 13661.97 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedNewton’s rings P2220200


� Coherent light� Phase relationship� Path difference� Interference in thin films� Newton’s ring apparatus

LEP_2 09.08.2007 11:42 Uhr Seite 93


Principle:Monochromatic light falls on a planeparallel mica plate. The light rays,reflected at the front surface as wellas at the rear surface, will interfereto form a pattern of concentric rings.The radii of the rings depend on thegeometry of the experimental set-up, the thickness of the mica plateand the wavelength of the light.

Interference order m as a function of sin2� for Na-light.

Tasks:The experiment will be performedwith the light of a Na-lamp and withthe light of different wavelengths ofa Hg-vapour tube.

1. The thickness of the mica plate isdetermined from the radii of theinterference rings and the wave-length of the Na-lamp.

2. The different wavelengths of theHg-vapour tube are determinedfrom the radii of the interferencerings and the thickness of themica plate.


� Interference of equalinclination

� Interference of thin layers� Plane parallel plate� Refraction� Reflection� Optical path difference

Mica plate 08558.00 1

Colour filter, 440 nm 08411.00 1




Spectral lamp Na, pico 9 base 08120.07 1



Plate holder with tension spring 08288.00 2









What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference at a mica plate according to Pohl P2220300


Optics Interference

LEP_2 09.08.2007 11:42 Uhr Seite 94


Interference Optics

Fresnel’s zone construction / zone plate 2.2.04-00

Principle:A zone plate is illuminated with par-allel laser light. The focal points ofseveral orders of the zone plate areprojected on a ground glass screen.

Geometry of the zone plate.

Tasks:1. The laser beam must be widened

so that the zone plate is well illu-minated. It must be assured thatthe laser light beam runs parallelover several meters.

2. The focal points of several ordersof the zone plate are projected ona ground glass screen. The focallengths to be determined are plot-ted against the reciprocal value oftheir order.

3. The radii of the zone plate are cal-culated.

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1

Fresnel zone plate, after Fresnel 08577.03 1


Lens, mounted, f = +20 mm 08018.01 1

Lens, mounted, f = +50 mm 08020.01 1

Lens, mounted, f = +100 mm 08021.01 1

Lens, mounted, f = -50 mm 08026.01 1

Object holder 50 mm x 50 mm 08041.00 2

Ground glass screen, 50 mm d = 50 mm 08136.01 1

Polarisation filter, 50 mm, d = 50 mm 08613.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedFresnel’s zone construction / zone plate P2220400


� Huygens-Fresnel principle� Fresnel and Fraunhofer

diffraction� Interference� Coherence� Fresnel’s zone construction� Zone plates

LEP_2 09.08.2007 11:42 Uhr Seite 95


Principle:In the Michelson arrangement inter-ference will occur by the use of 2mirrors. The wavelength is deter-mined by displacing one mirror usingthe micrometer screw.

Formation of circles on interference.

Tasks:Determination of the wavelength ofthe light of the used laser.


� Interference� Wavelength� Refractive index� Velocity of light� Phase� Virtual light source

Michelson interferometer 08557.00 1

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1


Lens, mounted, f = +20 mm 08018.01 1

Lens mounted, f = +5 mm 08017.01 1







What you need:


Optics Interference

ADVANCED OPTICSAND LASER PHYSICS

You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

Complete Equipment Set, Manual on CD-ROM includedMichelson interferometer P2220500

LEP_2 09.08.2007 11:42 Uhr Seite 96


Interference Optics

Coherence and width of spectral lines with Michelson interferometer 2.2.06-00

Principle:The wavelengths and the corre-sponding lengths of coherence of thegreen spectral lines of an extremehigh pressure Hg vapour lamp aredetermined by means of a Michelsoninterferometer.

Different double slit combinationsare illuminated to verify the coher-ence conditions of non punctuallight sources. An illuminated auxil-iary adjustable slit acts as a nonpunctual light source.

Beam path in Michelson’s interferometer.

Tasks:1. Determination of the wavelength

of the green Hg spectral line aswell as of its coherence length.

2. The values determined in 1. areused to calculate the coherencetime and the half width value ofthe spectral line.

3. Verification of the coherence con-dition for non punctual lightsources.

Michelson Interferometer 08557.00 1

High pressure mercury vapour lamp CS 50 W 08144.00 1

Power supply for Hg-CS/50 W Lamp 13661.97 1

Optical profile bench, l = 100 cm 08282.00 1

Base for optical profile bench 08284.00 2

Slide mount, h = 30 mm 08286.01 5


Object holder 50 x 50 mm 08041.00 1

Swingin arm 08256.00 1



Mounted lens f = 20 mm 08018.01 1

Mounted lens f = 200 mm 08024.01 1

Iris diaphragm 08045.00 1

Coloured filter, green, 525 nm 08414.00 1

Ground-glass screen 50 x 50 mm 08136.01 1

Diaphragm holder, attachable 11604.09 1

Measuring magnifier 09831.00 1

Slit, adjustable up to 1 mm 11604.07 1

Diaphragm with 4 double slits 08523.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedCoherence and width of spectral lineswith Michelson interferometer P2220600


� Fraunhofer and Fresnel dif-fraction

� Interference� Spatial and time coherence� Coherence conditions� Coherence length for non

punctual light sources� Coherence time� Spectral lines (shape and half

width value)� Broadening of lines due to

Doppler effect and pressurebroadening

� Michelson interferometer� Magnification

LEP_2 09.08.2007 11:42 Uhr Seite 97


Principle:A measurement cuvette set in thebeam path of a Michelson interfe-rometer can be evacuated or filledwith CO2. The refraction indexes ofair or CO2 are determined throughthe assessed modification of theinterference pattern.

Number N of minima changes as a function of air pressure in the measuringcuvette.


� Interference� Wavelength� Phase� Refraction index� Light velocity� Virtual light source

Michelson interferometer 08557.00 1

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1

Glass cell, diam. 21,5 mm 08625.00 1

Manual vacuum pump with manometer 08745.00 1







Lens mounted, f = +5 mm 08017.01 1

Compressed gas, CO2, 21 g 41772.06 1

Fine control valve for pressure bottles 33499.00 1




Tubing connect., Y-shape, d = 8-9 mm 47518.03 1

PVC tubing, d = 7 mm 03985.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedRefraction index of air and CO2with Michelson interferometer P2220700


Optics Interference


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

LEP_2 09.08.2007 11:42 Uhr Seite 98


Diffraction Optics

Diffraction at a slit and Heisenberg’s uncertainty principle 2.3.01-00

Principle:The distribution of intensity in theFraunhofer diffraction pattern of aslit is measured. The results are eval-uated both from the wave patternviewpoint, by comparison withKirchhoff’s diffraction formula, andfrom the quantum mechanics stand-point to confirm Heisenberg’s uncer-tainty principle.

Tasks:1. To measure the intensity distri-

bution of the Fraunhofer diffrac-tion pattern of a single slit (e. g.0.1 mm).The heights of the maxima andthe positions of the maxima andminima are calculated accordingto Kirchhoff’s diffraction formulaand compared with the measuredvalues.

Intensity in the diffraction pattern of a 0.1 mm wide slit at a distance of 1140 mm. The photocurrent is plotted as a function of the position.

2. To calculate the uncertainty ofmomentum from the diffractionpatterns of single slits of differingwidths and to confirm Heisen-berg’s uncertainty principle.

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1

Diaphragm with 3 single slits 08522.00 1


Diaphragm with 4 multiple slits 08526.00 1


Photoelement for optical base plate 08734.00 1



Universal measuring amplifier 13626.93 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction at a slit and Heisenberg’suncertainly principle P2230100


� Diffraction� Diffraction uncertainty� Kirchhoff’s diffraction formula� Measurement accuracy� Uncertainty of location� Uncertainty of momentum� Wave-particle dualism� De Broglie relationship

LEP_2 09.08.2007 11:42 Uhr Seite 99


Principle:Monochromatic light is incident on aslit or an edge. The intensity distribu-tion of the diffraction pattern isdetermined.

Intensity distribution on diffraction at the slit, as a function of the positionalong a straight line parallel to the plane of the slit, standardised on theintensity without the slit.

Tasks:1. Measurement of the width of a

given slit.

2. Measurement of the intensity dis-tribution of the diffraction patternof the slit and

3. of the edge.


� Intensity� Fresnel integrals� Fraunhofer diffraction

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1Photoelement for optical base plate 08734.00 1Lens holder 08012.00 1Lens, mounted, f = -50 mm 08026.01 1Slit, adjustable 08049.00 1Screen, metal, 300 mm x 300 mm 08062.00 1Barrel base -PASS- 02006.55 4Meter Scale, l = 1000 x 27 mm 03001.00 1G-clamp 02014.00 1Measuring tape, l = 2 m 09936.00 1Multi-range meter with amplifier 07034.00 1

*Alternative:Universal measuring amplifier 13625.93 1Digital multimeter 2010 07128.00 1Connecting cord, l = 75 cm, red 07362.01 1Connecting cord, l = 75 cm, blue 07362.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction of light at a slit and an edge P2230200


Optics Diffraction


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

LEP_2 09.08.2007 11:42 Uhr Seite 100


Diffraction Optics

Intensity of diffractions due to pin hole diaphragms and circular obstacles 2.3.03-00

Principle:Pin hole diaphragms and circularobstacles are illuminated with laserlight. The resulting intensity distribu-tions due to diffraction are measuredby means of a photo diode.

Tasks:1. The complete intensity distribu-

tion of the diffraction pattern of apin hole diaphragm (D1 = 0.25mm) is determined by means of asliding photo diode. The diffrac-tion peak intensities are comparedwith the theoretical values. Thediameter of the pin hole dia-phragm is determined from thediffraction angles of peaks andminima.

2. The positions and intensities ofminima and peaks of a second pinhole diaphragm (D2 = 0.5 mm) are

Diffracted intensity I vs position x of the photodiode, using a diaphragm withD1 = 0.25 mm.

determined. The diffraction peakintensities are compared with thetheoretical values. The diameter ofthe pin hole diaphragm is deter-mined.

3. The positions of minima and peaksof the diffraction patterns of twocomplementary circular obstacles(D*1 = 0.25 mm and D*2 = 0.5mm) are determined. Results arediscussed in terms of Babinet’sTheorem.

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1








Screen with diffracting elements 08577.02 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedIntensity of diffractions due to pin holediaphragms and circular obstacles P2230300


� Huygens principle� Interference� Fraunhofer and Fresnel

diffraction� Fresnel’s zone construction� Coherence� Laser� Airy disk� Airy ring� Poisson’s spot� Babinet’s theorem� Bessel function� Resolution of optical

instruments

LEP_2 09.08.2007 11:42 Uhr Seite 101

2.3.04-00 Diffraction intensity of multiple slits and grids

Principle:Multiple slits which all have thesame width and the same distanceamong each other, as well as trans-mission grids with different grid con-stants, are submitted to laser light.The corresponding diffraction pat-terns are measured according totheir position and intensity, bymeans of a photo diode which can beshifted.

Tasks:1. The position of the first intensity

minimum due to a single slit isdetermined, and the value is usedto calculate the width of the slit.

2. The intensity distribution of thediffraction patterns of a three-fold, fourfold and even a fivefoldslit, where the slits all have thesame widths and the same dis-tance among each other, is to be

Diffraction intensity I as a function of the position x for a threefold slit, b1 = 0.1 mm and g = 0.25 mm. Distance between threefold slit and photo-cell: L = 107 cm. For comparison, the intensity distribution of a single slit, b = 0.1 mm, is entered as a dotted line.

determined. The intensity relationsof the central peaks are to beassessed.

3. For transmission grids with differ-ent lattice constants, the positionof the peaks of several orders ofdiffraction is to be determined,and the found value used to cal-culate the wavelength of the laserlight.


� Huygens principle� Interference� Fraunhofer und Fresnel

diffraction� Coherence� Laser

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1








Lens, mounted, f = +20 mm 08018.01 1

Lens, mounted, f = +100 mm 08021.01 1



Diaphragm with 4 multiple slits 08526.00 1



Diffraction grating,10 lines/mm 08540.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction intensityof multiple slits and grids P2230400


Optics Diffraction

LEP_2 09.08.2007 11:42 Uhr Seite 102


Diffraction Optics

Determination of the diffraction intensity at slit and double slit systems 2.3.05-00

Principle:Slit and double slit systems are illu-minated with laser light. The corre-sponding diffraction patterns aremeasured by means of a photodiodewhich can be shifted, as a functionof location and intensity.

Tasks:1. Determination of the intensity

distribution of the diffraction pat-terns due to two slits of differentwidths.The corresponding width of theslit is determined by means of therelative positions of intensity val-ues of the extremes. Furthermore,intensity relations of the peaks areevaluated.

Diffraction intensity I as a function of location x for the single slit b1 = 0.1 mm and b2 = 0.2 mm.The x axis of the graph for b1 = 0.1 mm is shifted upwards. The intensity ofthe areas next to the central peak is represented enlarged by a factor of 10.(Distance between slit and photodiode L = 107 cm; � = 632.8 nm).

2. Determination of location andintensity of the extreme values ofthe diffraction patterns due totwo double slits with the samewidths, but different distancesbetween the slits. Widths of slitsand distances between the slitsmust be determined as well as theintensity relations of the peaks.

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1








Lens, mounted, f = +20 mm 08018.01 1

Lens, mounted, f = +100 mm 08021.01 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedDetermination of diffraction intensityat slit and double slit systems P2230500


� Huygens principle� Interference� Fraunhofer and Fresnel

diffraction� Coherence� Laser


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

LEP_2 09.08.2007 11:42 Uhr Seite 103


Principle:An aperture consisting of a single slitand a complementary strip (wire) isilluminated with a laser beam. Thecorresponding diffraction patternsare measured according to positionand intensity with a photocell whichcan be shifted.

Tasks:1. Determination of the intensity

distribution of the diffraction pat-terns due to a slit and comple-mentary strip (wire).

2. Determination of the intensityrelations of the diffraction patternpeaks for the single slit.

Diffraction intensity I as a function of the position x for single slit a) andstrip b). Width of the diffracting object b = 0.2 mm.The intensities in the areas next to the central peak are represented extend-ed by a factor of 10. (Distance between diffracting object and photocellL=120cm; Wavelength of the laser light � = 632.8 nm)

3. Babinet’s theorem is discussedusing the diffraction patterns ofthe slit and the complimentarystrip.


� Huygens’ principle� Interference� Fraunhofer und Fresnel

diffraction� Babinet’s theorem� Poissons’ spot� Coherence� Laser

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1


Optical profile bench l = 150 cm 08281.00 1

Base f. opt. profile-bench, adjust. 08284.00 2

Slide mount f. opt. pr.-bench, h = 30 mm 08286.01 3

Slide device, horizontal 08713.00 1

Object holder, 5 x 5 cm 08041.00 1

Photoelement f. opt. base plt. 08734.00 1

Screen, with diffracting elements 08577.02 1


Connecting cable, l = 750 mm, red 07362.01 1

Connecting cable, l = 750 mm, blue 07362.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction intensity through a slit and a wire – Babinet’s theorem P2230600


Optics Diffraction


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

LEP_2 09.08.2007 11:42 Uhr Seite 104


Photometry Optics

Photometric law of distance 2.4.02-01

Principle:The luminous intensity emitted by apunctual source is determined as afunction of distance.

Illuminance as a function of the reciprocal values of the square of the dis-tances.

Tasks:1. The luminous intensity emitted by

a punctual source is determined asa function of distance from thesource.

2. The photometric law of distance isverified by plotting illuminance asa function of the reciprocal valueof the square of the distance.


� Luminous flux� Quantity of light� Luminous intensity� Illuminance� Luminance

Hand held measuring instrument Lux, RS 232 07137.00 1

Luxmeter probe 12107.01 1





Lamp socket E 14, on stem 06175.00 1

Filament lamps, 6 V/5 A 06158.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedPhotometric law of distance P2240201

LEP_2 09.08.2007 11:42 Uhr Seite 105



Principle:The luminous intensity emitted by apunctual source is determined as afunction of distance.

Experimental objective:The luminous intensity is a functionof the distance of the light sensorfrom the light source. The law forpoint light sources on which this isbased should be determined.

Luminous intensity as a function of the square of the reciprocal of the dis-tance (lamp – diode)

Tasks:1. The luminous intensity emitted by

a punctual source is determined asa function of distance from thesource.

2. The photometric law of distance isverified by plotting illuminance asa function of the reciprocal valueof the square of the distance.




Lamp socket E 14, on stem 06175.00 1

Filament lamps, 6 V/5 A 06158.00 1



Distributor 06024.00 1



Meter Scale, l = 1000 x 27 mm 03001.00 1

Photo diode, G1 39119.01 1












What you need:

Complete Equipment Set, Manual on CD-ROM includedPhotometric law of distance with Cobra3 P2240211

Optics Photometry


� Luminous flux� Quantity of light� Luminous intensity� Illuminance� Luminance

LEP_2 09.08.2007 11:42 Uhr Seite 106


Photometry Optics

Lambert’s law 2.4.04-00

Principle:Visible light impinges on a diffuselyreflecting surface. The luminance ofthis surface is determined as a func-tion of the angle of observation.

Illuminance as a function of cos �.

Tasks:1. The luminous flux emitted reflect-

ed by a diffusely reflecting surfaceis to be determined as a functionof the angle of observation.

2. Lambert’s law (cos-law) is to beverified using the graph of themeasurement values.

Housing for experiment lamp 08129.01 1

Halogen lamp, 12 V/50 W 08129.06 1

Holder G 6.35 for 50/100 W halogen lamp 08129.04 1



Lens, mounted, f = +200 mm 08024.01 1

Zinc sulphide screen, 90 mm x 120 mm 08450.00 1








Articulated radial holder 02053.01 1

Graduated disk, for demonstration 02053.02 1



Luxmeter probe 12107.01 1

Hand held measuring instrument Lux, RS 232 07137.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedLambert’s law P2240400


� Luminous flux� Light quantity� Light intensity� Illuminance� Luminance

LEP_2 09.08.2007 11:42 Uhr Seite 107

2.5.01-00 Polarisation by quarterwave plates

Principle:Monochromatic light falls on a micaplate perpendicular to its optic axis.At the appropriate plate thickness(�/4, or quarter-wave plate) there isa 90 ° phase shift between the ordi-nary and the extraordinary ray whenthe light emerges from the crystal.The polarisation of the emergentlight is investigated at differentangles between the optic axis of the�/4 plate and the direction of pola-risation of the incident light.

Tasks:1. To measure the intensity of plane-

polarised light as a function of theposition of the analyser.

2. To measure the light intensitybehind the analyser as a functionof the angle between the opticaxis of the �/4 plate and that ofthe analyser.

Intensity distribution of polarised light as a function of the direction of trans-mission of the analyser: with �/4 plate at various angular settings.

3. To perform experiment 2. with two�/4 plates one behind the other.


� Plane� Circularly and elliptically

polarised light� Polariser� Analyzer� Plane of polarisation� Double refraction� Optic axis� Ordinary and extraordinary

ray



Lens, mounted, f = +100 mm 08021.01 1


Iris diaphragm 08045.00 1



Mercury vapour high pressure lamp, 50 W 08144.00 1

Power supply 230V/50 Hz for 50 W Hg-lamp 13661.97 1

Interference filter yellow, 578 nm 08461.01 1

Polarisation filter on stem 08610.00 2





Polarisation specimen, mica 08664.00 2





What you need:

Complete Equipment Set, Manual on CD-ROM includedPolarisation by quarterwave plates P2250100


Optics Photometry

LEP_2 09.08.2007 11:42 Uhr Seite 108


Polarisation Optics

Polarimetry 2.5.02-00

Principle:The rotation of the plane of polarisa-tion through a sugar solution meas-ured with a half-shade penumbrapolarimeter and the reaction rateconstant for the inversion of canesugar determined.

Semi-logarithmic plot of the measured values from cane sugar inversion.

Tasks:1. To determine the specific rotation

of cane sugar (sucrose) and lac-tose by measuring the rotation ofvarious solutions of known con-centration.

2. To determine the reaction rateconstant when cane sugar istransformed into invert sugar.

Half-shade polarimeter, 230 V AC 35906.93 1





Crucible tongs, l = 200 mm, stainless steel 33600.00 1

Beaker, 250 ml, low form, plastic 36013.01 2

Graduated cylinder, 100 ml, plastic 36629.01 2

Graduated vessel, 1 l, with handle 36640.00 1

Funnel, plastic, d = 100 mm 36891.00 1

Spoon with spatula end, l = 180 mm, PA, wide 38833.00 1

Stirring rods, BORO 3.3, l = 300 mm, d = 8 mm 40485.06 1

Pipette, with rubber bulb, long 64821.00 1

D (+)-Sucrose, 100 g 30210.10 1

Hydrochloric acid 37 %, 1000 ml 30214.70 1


D(+)-Lactose, powder 100 g 31577.10 1

Balance LG 311, 4 beams 44007.31 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedPolarimetry P2250200


� Half-shade principle� Optical rotatory power� Optical activity� Saccharimetry� Specific rotation� Reaction rate� Weber-Fechner law

LEP_2 09.08.2007 11:42 Uhr Seite 109


0.8

0.6

0.4

0.2

20° 40° 60° 80°

EXP.

THEOR.

�

�

�

�

''

� �p

Principle:Plane-polarized light is reflected at aglas surface. Both the rotation of theplane of polarization and the inten-sity of the reflected light are to bedetermined and compared withFrewsnel’s formulae for reflection.

Tasks:1. The reflection coefficients for light

polarized perpendicular and par-allel to the plane of incidence areto be determined as a function ofthe angle of incidence and polttedgraphically.

2. The refractive index of the flintglass prism is to be found.

3. The reflection coefficients are tobe calculated using Fresnel’s for-mulae and compared with themeasured curves.

Measured and calculated curves for�r" and �r� as a function of the angle of

incidence.

4. The reflection factor for the flintglass prism is to be calculated.

5. The rotation of the polarizationplane for plane polarized lightwhen reflected is to be deter-mined as a function of the angleof incidence and presented graph-ically. It is then to be comparedwith values calculated using Fres-nel’s formulae.


� Electromagnetic theory oflight

� Reflection coefficient� Reflection factor� Brewster’s law� Law of refraction� Polarization� Polarization level

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1


Prism, 60 degrees, h = 36 mm, flint 08237.00 1

Prism table with holder 08254.00 1


Protractor scale with pointer 08218.00 1




H-base -PASS- 02009.55 2




Multi-range meter with amplifier 07034.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFresnel’s equations – theory of reflection P2250300


Optics Polarisation


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

LEP_2 09.08.2007 11:42 Uhr Seite 110


Polarisation Optics

Malus’ law 2.5.04-00

Principle:Linear polarized light passes througha polarization filter.

Transmitted light intensity is deter-mined as a function of the angularposition of the polarization filter.

Corrected photo cell current as a function of the angular position � of the po-larization plane of the analyzer.

Tasks:1. The plane of polarization of a lin-

ear polarized laser beam is to bedetermined.

2. The intensity of the light transmit-ted by the polarization filter is tobe determined as a function of theangular position of the filter.

3. Malus’ law must be verified.

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedMalu’s law P2250400


� Electric theory of light� Polarization� Polarizer� Analyzer� Brewster's law� Malus' law


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

LEP_2 09.08.2007 11:42 Uhr Seite 111


Principle:The angle of rotation of the polarisa-tion-plane of plane polarized lightthrough a flint glass rod is found tobe a linear function of the product ofthe mean flux-densitiy and thelength of the optical medium. Thefactor of proportionally, calledVerdet’s constant, is investigated asa function of the wavelength and theoptical medium.

Tasks:1. To determine the magnetic flux-

densitiy between the pole piecesusing the axial Hall probe of theteslameter for different coil cur-rents. The mean flux-density iscalculated by numerical integra-tion and the ratio maximum flux-density over mean flux-density es-tablished.

2. To measure the maximum flux-density as a function of the coilcurrent and to establish the rela-tionship between mean flux-den-sity and coil current anticipatingthat the ratio found under 1. re-mains constant.

Verdet’s constant as a function of the wavelength+ measured values --- theoretical values.

3. To determine the angle of rotationas a function of the mean flux-density using different colour fil-ters. To calculate the correspond-ing Verdet’s constant in each case.

4. To evaluate Verdet’s constant as afunction of the wavelength.


� Electromagnetic fieldinteraction

� Electron oscillation� Electromagnetism� Polarization� Verdet’s constant� Hall effect

Glass rod for Faraday effect 06496.00 1Coil, 600 turns 06514.01 2Pole pieces, drilled 06495.00 1Iron core, U-shaped, laminated 06501.00 1Housing for experiment lamp 08129.01 1Halogen lamp, 12 V/50 W 08129.06 1Holder G 6.35 for 50/100 W halogen lamp 08129.04 1Double condenser, f = 60 mm 08137.00 1Variable transformer 25 V~/20 V-, 12 A 13531.93 1Ampermeter, 1 mA...3 A DC/AC 07036.00 1Commutator switch 06034.03 1Teslameter, digital 13610.93 1Hall probe, axial 13610.01 1Lens, mounted, f = +150 mm 08022.01 1Lens holder 08012.00 1Table top on rod 08060.00 1Object holder 50 mm x 50 mm 08041.00 1Colour filter, 440 nm 08411.00 1Colour filter, 505 nm 08413.00 1Colour filter, 525 nm 08414.00 1Colour filter, 580 nm 08415.00 1Colour filter, 595 nm 08416.00 1Polarisation filter with vernier 08611.00 2Screen, translucent, 250 mm x 250 mm 08064.00 1Optical profile bench, l = 1000 mm 08282.00 1Base for optical profile bench, adjustable 08284.00 2Slide mount for optical profil bench, h = 30 mm 08286.01 2Slide mount for optical profil bench, h = 80 mm 08286.02 5Universal clamp 37718.00 1Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 3Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedFaraday effect P2260100


Optics Applied Optics

LEP_2 09.08.2007 11:42 Uhr Seite 112


Applied Optics Optics

Kerr effect 2.6.02-00

Principle:Monochromatic, vertically polarizedlight impinges on a PLZT element(lead-lanthanum-zirconium-titani-um compount) which is set in itsholder at 45 ° to the vertical.

An electric field is applied to thePLZT element and causes it tobecome birefractive. The phase-shiftbetween the normal and the extraor-dinary light beam behind the PLZTelement is recorded as a function ofthe applied voltage and it is shownthat the phase-shift is proportionalto the square of the electric fieldstrength respectively of the voltageapplied. From the constant of pro-

portionality the Kerr constant is cal-culated for the PLZT element.

The Kerr effect has usually beendemonstrated with nitrobenzene inthe past. Since nitrobenzene is verytoxic and needs high voltages ofsome kV the PLZT element whichonly needs some hundred volts rep-resents an attractive alternative.

Relative luminous intensity behind the analyser as a function of the volt-II0

Tasks:1. The phase-shift between the nor-

mal and the extra-ordinary lightbeam is to be recorded for differ-ent voltages applied to the PLZT-element respectively for differentelectric field strengs. The half-wave voltage U is to be deter-mined.

2. By plotting the square of theapplied voltage versus the phaseshift between normal and extraor-dinary beam it is to be shown thatthe relation between the twoquantities is approximately linear.From the slope of the straight linethe Kerr constant is to be calcu-lated.

(l2)

Kerr cell, PLZT element 08641.00 1

High voltage supply 0...10 kV 13670.93 1

Laser, He-Ne 1.0 mW, 230 VAC 08181.93 1













What you need:

Complete Equipment Set, Manual on CD-ROM includedKerr effect P2260200


� Polarization of light� Birefraction� Optical anisotropy� Modulation of light� Electro-optical modulator� PLZT-element


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

age U applied to the PLZT element and the phase-shift � between normaland extraordinary beam.

LEP_2 09.08.2007 11:42 Uhr Seite 113


Principle:In contrast to normal photography ahologram can store information aboutthe three-dimensionality of an object.To capture the three-dimensionalityof an object, the film stores not onlythe amplitude but also the phase ofthe light rays. To achieve this, a co-herent light beam (laser light) is splitinto an object and a reference beamby being passed through a beam split-ter. These beams interfere in the planeof the holographic film. The hologramis reconstructed with the referencebeam which was also used to recordthe hologram.

Setup for recording and reconstruction of a transmission hologram.

Tasks:1. Capture the holographic image of

an object.

2. Perform the development andbleaching of this phase hologram.

3. Reconstruct the transmissionhologram (reconstruction beam isthe reference beam during imagecapture).


� Object beam� Reference beam� Real and virtual image� Phase holograms� Amplitude holograms� Interference� Diffraction� Coherence� Developing of film

Complete Equipment Set, Manual on CD-ROM includedRecording and reconstruction of holograms P2260300



Base plate in experimental case 08700.01 1He/Ne Laser, 5mW with holder 08701.00 1Power supply for laser head 5 mW 08702.93 1Magnetic foot for optical base plate 08710.00 6Holder for diaphragm/ beam plitter 08719.00 2Sliding device, horizontal 08713.00 1XY-shifting device 08714.00 2Adapter ring device 08714.01 1Achromatic objective 20 x N.A.0.4 62174.20 1Pin hole 30 micron 08743.00 1Adjusting support 35 x 35 mm 08711.00 2Surface mirror 30 x 30 mm 08711.01 2Surface mirror,large, d = 80 mm 08712.00 1Beam plitter 1/1, non polarizing 08741.00 1Object for holography 08749.00 1Holographic plates, 20 pcs.* 08746.00 1Darkroom equipment for holography 08747.88 1

consisting of:

Plastic trays, 4 pcs. • Laboratory gloves, medium, 100 pcs. • Tray thermome-ter, offset, +40°C • Roller squeegee • Clamps, 2 pcs. • Film tongs, 2 pcs. •Darkroom lamp with green filter • Light bulb 230 V/15 W • Funnel •Narrow-necked bottles, 4 pcs.

Set of photographic chemicals 08746.88 1Consisting of: Holographic developer • Stop bath • Wetting agent •Laminate; Paint

Bleaching chemicals:Potassium dichromate, 250 g 30102.25 1Sulphuric acid, 95-98%, 500 ml 30219.50 1

*Alternative:Holographic sheet film 08746.01 1Glass plate, 120 x 120 x 2 mm 64819.00 2

What you need:

LEP_2 09.08.2007 11:42 Uhr Seite 114



CO2-laser 2.6.04-00

Principle:Among molecular laser, the CO2-laseris of greatest practical importance.The high level of efficiency with whichlaser radiation can be generated incontinuous wave (cw) and pulse oper-ation is its most fascinating feature.The experimental equipment set is anopen CO2-didactic laser system ofmax. 8 W power output. Since it is an“open” system, all components of thesystem can be handled individuallyand the influence of each procedureon the output power can be studied.One very primary and essential targetin learning is the alignment of theCO2-laser by means of a He-Ne-laser.

Tasks:1. Align the CO2-laser and optimize

its power output.

2. Check the influence of the Brew-ster windows position on thepower output.

3. Determine the power output as afunction of the electric powerinput and gasflow.

4. Evaluate the efficiency as a func-tion of the electric power inputand gasflow.

Laser power as a function of the angle of inclination of the brewster windownormal N.

5. If the gas-mixing unit is suppliedthe influence of the differentcomponents of the laser gas (CO2,He, N2) to the output efficiency ofthe CO2-laser are analyzed.

6. Measurement of temperaturesdifferences for the laser gas(imput / output) for study of con-version efficiency.

CO2-laser tube, detachable, typically 5 W 08596.00 1Module box for CO2-laser tube 08597.00 1Set of laser mirrors, ZnSe and Si 08598.00 1Optical bench on steel rail, l = 1,3 m 08599.00 1HV-power supply 5 kV/50 mA DC 08600.93 1Ballast resistor unit incl. 3 HV cables 08601.00 1Cooling water unit, portable 08602.93 1Rotatory vane vacuum pump, two stages 02751.93 1Gas filter/buffer unit 08605.00 1He/Ne-laser/adjusting device 08607.93 1Diaphragm for adjusting CO2 Laser 08608.00 2Screen, translucent, 250 mm x 250 mm 08064.00 1Right angle clamp -PASS- 02040.55 1Powermeter 30 mW/10 Watt 08579.93 1Support for power probe 08580.00 1Protection glasses, 10.6 micro-m 08581.00 1Cleaning set for laser 08582.00 1ZnSe biconvex lens, d = 24 mm, f = 150 mm 08609.00 1Digital Thermometer, 2 x NiCr-Ni 07050.01 1HV-isolated temperature probe 08584.00 1Control panel with support, 1 gas* 08606.00 1Pressure control valve 200/3 bar, CO2/He* 08604.01 1Laser gas in bottle, 50 l/200 bar* 08603.00 1

*Alternative to:Laser gas mixing unit, 3 gases 08606.88 1

Option: Experiment set for laser beam analysis 08610.10 1

1. Estimation of wavelength by diffraction grating and2. Distribution of power by diaphragm

IR conversion plate for observation of CO2-laser infrared radiation 08611.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedCO2-laser P2260400


� Molecular vibration� Exitation of molecular

vibration� Electric discharge� Spontaneous emission� Vibration niveau� Rotation niveau� Inversion� Induced emission� Spectrum of emission� Polarization� Brewster angle� Optical resonator

LEP_2 09.08.2007 11:42 Uhr Seite 115


Principle:Small particles in a current passthrough the LDA measuring volumeand scatter the light whose frequen-cy is shifted by the Doppler effectdue to the particle movement.

The frequency change of the scat-tered light is detected and convertedinto a particle or flow velocity.

Measurement of the signal spectrum with a signal peak


� Interference� Doppler effect� Scattering of light by small

particles (Mie scattering)� High- and low-pass filters� Sampling theorem� Spectral power density� Turbulence



Tasks:1. Measurement of the light-fre-

quency change of individual lightbeams which are reflected bymoving particles.

2. Determination of the flow veloci-ties.

Optical base plate with rubberfeet 08700.00 1He/Ne Laser, 5 mW with holder 08701.00 1Power supply for laser head 5 mW 08702.93 1Adjusting support 35 x 35 mm 08711.00 2Surface mirror 30 x 30 mm 08711.01 2Magnetic foot for optical base plate 08710.00 8Holder for diaphragm/ beam plitter 08719.00 1Lens, mounted, f = +100 mm 08021.01 1Lens, mounted, f = +50 mm 08020.01 1Lens, mounted, f = +20 mm 08018.01 1Iris diaphragm 08045.00 1Beam plitter 1/1, non polarizing 08741.00 1Si-Photodetector with Amplifier 08735.00 1Control Unit for Si-Photodetector 08735.99 1Adapter BNC socket/4 mm plug pair 07542.27 1Screened cable, BNC, l = 750 mm 07542.11 1Prism table with holder for optical base plate 08725.00 1Lens holder for optical base plate 08723.00 3Screen, white, 150 x 150 mm 09826.00 1XY-shifting device 08714.00 1Pin hole 30 micron 08743.00 1LDA-Accessory-Set 08740.00 1Support rod -PASS-, square, l = 630 mm 02027.55 2Right angle clamp -PASS- 02040.55 2Universal clamp 37718.00 2Support base -PASS- 02005.55 1Aspirator bottle, clear glass, 1000 ml 34175.00 2Silicone tubing, d = 7 mm 39296.00 4Pinchcock, width 10 mm 43631.10 3Glass tube, AR-glass, straight, d = 8 mm, l = 80 mm, 10 pcs. 36701.65 1Rubber stopper, d = 32/26 mm, 1 hole 39258.01 2Rubber stopper, d = 22/17 mm, 1 hole 39255.01 2Measuring tape, l = 2 m 09936.00 1Spatulas, double bladed, l = 150 mm, wide 33460.00 1Beaker, DURAN®, short form, 150 ml 36012.00 1Cobra3 BASIC-UNIT, USB 12150.50 1

What you need:

Power supply 12V/2A 12151.99 1Software Cobra3 Fourier Analysis 14514.61 1Sliding device, horizontal 08713.00 1PC, Windows® 95 or higher

Complete Equipment Set, Manual on CD-ROM includedLDA – Laser Doppler Anemometrywith Cobra3 P2260511

LEP_2 09.08.2007 11:42 Uhr Seite 116



Helium Neon Laser 2.6.07-01

Principle:The difference between spontaneousand stimulated emission of light isdemonstrated. The beam propagationwithin the resonator cavity of a He-Ne laser and its divergence are deter-mined, its stability criterion ischecked and the relative outputpower of the laser is measured as afunction of the tube’s position insidethe resonator and of the tube current.

The following items can be realizedwith advanced set 08656.02.By means of a birefringent tuner anda Littrow prism different wave-lengths can be selected and quanti-tatively determined if a monochro-mator is available.Finally you can demonstrate the ex-istence of longitudinal modes andthe gain profile of the He-Ne laserprovided an analysing Fabry Perotsystem is at your disposal.

Tasks:1. Set up the He-Ne laser. Adjust the

resonator mirrors by use of thepilot laser. (left mirror: VIS, HR,plane ; right mirror: VIS, HR, R =700 mm)

2. Check on the stability condition ofa hemispherical resonator.

Relative output power as a function of mirror spacing.

HeNe laser, basic set 08656.93 1

Photoelement, silicon 08734.00 1


Screen, white, 150 x 150 mm 09826.00 1

Danger sign “Laser” 06542.00 1




Protection glasses HeNe laser 08581.10 1

Cleaning set for laser 08582.00 1

Option:

Experimentation set Helium-Neon laser, advanced set 08656.02 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedHelium Neon Laser P2260701


� Spontaneous and stimulatedlight emission

� Inversion� Collision of second type� Gas discharge tube� Resonator cavity� Transverse and longitudinal

resonator modes� Birefringence� Brewster angle� Littrow prism� Fabry Perot Etalon

Helium Neon Laser, advanced set P2260705

3. Measure the integral relative out-put power as a function of thelaser tube’s position within thehemispherical resonator.

4. Measure the beam diameter with-in the hemispherical resonatorright and left of the laser tube.

5. Determine the divergence of thelaser beam.

6. Measure the integral relative out-put power as a function of thetube current.

The He-Ne laser can be tuned usinga BFT or a LTP. Longitudinal modescan be observed by use of a FabryPerot Etalon of low finesse. Remark:These points can only be coveredquantitatively if a monochromatorand an analysing Fabry Perot systemare available.


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 123)

LEP_2 09.08.2007 11:42 Uhr Seite 117


10 20 30 40 50 60

Prel

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

812,9 nm

817,3 nm

808,4 nm

804,4 nm

T°C

Principle:The visible light of a semiconductordiode laser is used to excite theneodymium atoms within a Nd-YAG(Neodymium-Yttrium AluminiumGarnet) rod. The power output of thesemiconductor diode laser is firstrecorded as a function of the injec-tion current. The fluorescent spec-trum of the Nd-YAG rod is then de-termined and the maon absorptionlines of the Nd-atoms are verified.Conclusively, the mean life-time ofthe 4F3/2-level of the Nd-atoms ismeasured in appoximation.

Relative fluorescent power of the Nd-YAG rod as a function of the diodetemperature (wavelength) for I = 450 mA.

Tasks:1. To determine the power output of

the semiconductor diode laser as afunction of the injection current.

2. To trace the fluorescent spectrumof the Nd-YAG rod pumped by thediode laser and to verify the mainabsorption lines of neodymium.

3. To measure the mean life-time ofthe 4F3/2-level of the Nd-atoms.

4. For further applications see ex-periment 2.6.09 “Nd-YAG laser”.


� Spontaneous emission� Induced emission� Mean lifetime of a

metastable state� Relaxation� Inversion� Diode laser

Basic set optical pumping 08590.93 1

Sensor for measurement of beam power 08595.00 1




Protection glasses for Nd-YAG laser 08581.20 1

Optional:

Optical base plate in exp. case 08700.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedOptical pumping P2260800



LEP_2 09.08.2007 11:42 Uhr Seite 118



Nd-YAG laser 2.6.09-00

25

20

15

10

5

50 100 150

PNd-YAGmW

Pump powermW

From graphic:Threshold power = 57 mW

From graphic:Slope efficiency: 30%

Principle:The rate equation model for an opti-cally pumped four-level laser systemis determined. As lasing medium, aNd-YAG (Neodymium-Yttrium Alu-minium Garnet) rod has been select-ed which is pumped by means of asemiconductor diode laser.

The IR-power output of the Nd-YAGlaser is measured as a function of theoptical power input and the slope ef-ficiency as well as the thresholdpower are determined.

Finally, a KTP-crystal is inserted intothe laser cavity and frequency dou-bling is demonstrated. The quadraticrelationship between the power ofthe fundamental wave and the beampower for the second harmonic isthen evident.

Nd-YAG laser power output as a function of the pump power � = 808.4 nm.

Tasks:1. Set up the Nd-YAG laser and opti-

mize its power output.

2. The IR-power output of the Nd-YAG laser is to be measured as afunction of the pump power. Theslope efficiency and the thresholdpower are to be determined.

3. Verify the quadratic relationshipbetweenthe power of the funda-mental wave, with � = 1064 nm,and the beam power of the secondharmonic with � = 532 nm.

Basic set optical pumping 08590.93 1

Sensor for measurement of beam power 08595.00 1

Nd-YAG laser cavity mirror/holder 08591.01 1

Laser cavity mirror frequency doubling 08591.02 1

Frequency doubling crystal in holder 08593.00 1

Filter plate, short pass type 08594.00 1




Protection glasses for Nd-YAG laser 08581.20 1

Cleaning set for laser 08582.00 1

Optional:

Optical base plate in exp. case 08700.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedNd-YAG laser P2260900


� Optical pumping� Spontaneous emission� Induced emission� Inversion� Relaxation� Optical resonator� Resonator modes� Polarization� Frequency doubling

LEP_2 09.08.2007 11:46 Uhr Seite 119


Principle:The beam of a laser diode is treatedin a way that it can be coupled intoa monomode fibre. The problemsrelated to coupling the beam intothe fibre are evaluated and verified.In consequence a low frequency sig-nal is transmitted through the fibre.The numerical aperture of the fibre isrecorded. The transit time of light

through the fibre is measured andthe velocity of light within the fibreis determined. Finally the measure-ment of the relative output power ofthe diodelaser as a function of thesupply current leads to the charac-teristics of the diodelaser such as“threshold energy” and “slopeefficiency”.

Tasks:1. Couple the laser beam into the

fibre and adjust the setting-up ina way that a maximum of output

Relative output power at the fibre end versus angle readout.

power is achieved at the exit ofthe fibre.

2. Demonstrate the transmission of aLF – signal through the fibre.

3. Measure the numerical apertureof the fibre.

4. Measure the transit time of lightthrough the fibre and determinethe velocity of light within thefibre.

5. Determine the relative outputpower of the diodelaser as a func-tion of the supply current.


� Total reflection� Diode laser� Gaussian beam� Monomode and multimode

fibre� Numerical aperture� Transverse and longitudinal

modes� Transit time� Threshold energy� Slope efficiency� Velocity of light

Experimentation Set Fibre Optics 08662.93 1


Oscilloscope 100 MHz, 2-channel 11451.99 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFibre optics P2261000



LEP_2 09.08.2007 13:42 Uhr Seite 120



Fourier optics – 2f Arrangement 2.6.11-00

Principle:The electric field distribution of lightin a specific plane (object plane) isFourier transformed into the 2 f con-figuration.

Experimental set-up for the fundamental principles of Fourier optic (2f set-up). *only required for the 5 mW laser!

Tasks:Investigation of the Fourier trans-form by a convex lens for differentdiffraction objects in a 2 f set-up.

Optical base plate with rubberfeet 08700.00 1

He/Ne Laser, 5mW with holder 08701.00 1

Power supply for laser head 5 mW 08702.93 1

Adjusting support 35 x 35 mm 08711.00 2

Surface mirror 30 x 30 mm 08711.01 2

Magnetic foot for optical base plate 08710.00 7

Holder for diaphragm/ beam plitter 08719.00 1

Lens, mounted, f = +150 mm 08022.01 1

Lens, mounted, f = +100 mm 08021.01 1

Lens holder for optical base plate 08723.00 2

Screen, white, 150 x 150 mm 09826.00 1



Achromatic objective 20 x N.A.0.4 62174.20 1


XY-shifting device 08714.00 2

Adapter ring device 08714.01 1

Pin hole 30 micron 08743.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedFourier optics– 2f Arrangement P2261100


� Fourier transform� Lenses� Fraunhofer diffraction� Index of refraction� Huygens’ principle

LEP_2 09.08.2007 11:48 Uhr Seite 121


Principle:The electric field distribution of lightin a specific plane (object plane) isFourier transformed into the 4fconfiguration by 2 lenses and opti-cally filtered with appropriate dia-phragms.

Tasks:1. Optical filtration of diffraction

objects in 4f set-up.

2. Reconstruction of a filtered image.


� Fourier transform� Lenses� Fraunhofer diffraction� Index of refraction� Huygens’ principle� Debye-Sears-effect







Holder for diaphragm/beam plitter 08719.00 2

Lens, mounted, f = +100 mm 08021.01 3


Screen, white, 150 x 150 mm 09826.00 1

Slide -Emperor Maximilian- 82140.00 1

Screen with arrow slit 08133.01 1



Diaphragms, d = 1, 2, 3 and 5 mm 09815.00 1



XY-shifting device 08714.00 2

Achromatic objective 20 x N.A.0.4 62174.20 1

Adapter ring device 08714.01 1

Pin hole 30 micron 08743.00 1



Glass cell, 150 x 55 x 100 mm 03504.00 1

Table with stem 09824.00 2


Bosshead 02043.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedFourier optics – 4f Arrangement –Filtering and reconstruction P2261200



Principle of the set-up for coherent optical filtration.

LEP_2 09.08.2007 11:48 Uhr Seite 122

Handbooks Optics



Advanced Optics and Laser Physics

Laser Physics I – Experiments with coherent light 01179.02

16 described ExperimentsPlease ask for a complete equipmentlist Ref. No. 227021 Diffraction of lightLP 1.1 (12166)Diffraction of light through a slit and atan edge.LP 1.2 (12167)Diffraction through a slit andHeisenberg’s uncertainty principle.LP 1.3 (12168)Diffraction of light through a double slitor by a grid. LP 1.4 (12169)Diffraction of light through a slit andstripes, Babinet’s theorem

2 Interference of lightLP 2.1 (12170)Fresnel mirror and biprismLP 2.2 (12171)Michelson interferometerLP 2.3 (12172)Newton’s rings

3 Polarisation of lightLP 3.1 (12173)Fresnel’s law, theory of reflectionLP 3.2 (12174)Polarisation through λ/4 platesLP 3.3 (12175)Half shadow polarimeter, rotation of pola-risation through an optically active mediumLP 3.3 (12176)Kerr effectLP 3.5 (12177)Faraday effect

4 Refraction of lightLP 4.1 (12178)Index of refraction n of a flint glass prismLP 4.2 (12179)Determination of the index of refractionof air with Michelson’s interferometerLP 4.3 (12180)Determination of the index of refractionof CO2 with Michelson’s interferometer

5 Law of radiationLP 5.1 (12181)Lambert’s law of radiation

Laser Physics IIHolography 01400.02

11 described ExperimentsPlease ask for a complete equipmentlist Ref. No. 22703LH 1 (12900)Fresnel zone plate

LH 2 (12901)White light hologram

LH 3 (12902)White light hologram with expansion system

LH 4 (12903)Transmission hologram

LH 5 (12904)Transmission hologram with expansion system

LH 6 (12905)Transfer hologram from a master hologram.

LH 7 (12906)Double exposure procedure

LH 8 12907)Time-averaging procedure I (with tuning fork).

LH 9 (12908)Time-averaging procedure II (with loudspeaker).

LH 10 12909)Real time procedure I (bending of a plate).

LH 11 (12910)Real time procedure II (oscillating plate).

Laser Physics IIIInterferometry 01401.02

18 described ExperimentsPlease ask for a complete equipmentlist Ref. No. 22704LI 1 (13066)Michelson interferometerLI 2 (13067)Michelson interferometer – high resolutionLI 3 (13068)Mach - Zehnder interferometerLI 4 (13069)Sagnac interferometerLI 5 (13070)Doppler-Effect with Michelson interferom.LI 6 (13071)Magnetostriction with Michelson interferometerLI 7 (13072)Thermal expansion of solids with Michelson interferometerLI 8 (13073)Refraction index of CO2-gas withMichelson interferometerLI 9 (13074)Refraction index of air with Michelson interferometerLI 10 (13075)Refraction index of air with Mach-Zehnder interferometerLI 11 (13076)Refraction index of of CO2-gas withMach-Zehnder interferometerLI 12 (13077)Fabry - Perot interferometer – determi-nation of the wavelength of laserlightLI 13 (13078)Fabry - Perot interferometer – optical resonator modesLI 14 (22611)Fourier optics –2 f arrangementLI 15 (22612)Fourier optics – 4 f arrangement, filteringand reconstructionLI 16 (13079)Optical determination of the velocity ofultrasound in liquids – phasemodulationof laserlight by ultrasonic wavesLI 17 (13080)LDA – Laser Doppler AnemometryLI 18 (13081)Twyman-Green interferometer

Advanced Opticsand Laser Physics 00117.02

23 described ExperimentsPlease ask for a complete equipmentlist Ref. No. 22614Laser PhysicsLEP (P2260700)Helium Neon LaserLEP (P2260400)CO2-laserLEP (P2260900)Nd-YAG-laser

Advanced OpticsLP 1.3 (P1216800)Diffraction of light through a double slit or by a gridLP 1.4 (P1216900)Diffraction of light through a slit and stripes, Babinet’s theoremLP 2.2 (P1217100)Michelson interferometerLP 2.3 (P1217200)Newton’s ringsLP 2.3 (P1217400)Polarisation through �/4 platesLP 3.4 (P1217600)Kerr effectLP 3.5 (P1217700)Faraday effectLP 4.3 (P1218000)Determination of the index of refractionof CO2 with Michelson’s interferometerLH 3 (P1290200)White light hologram with expansionsystemLH 5 (P1290400)Transmission hologram with expansionsystemLH 6 (P1290500)Transfer hologram from a master hologramLH 10 (P1290900)Real time procedure I (bending of a plate)LI 3 (P1306700)Michelson interferometer – High ResolutionLI 5 (P1307000)Doppler effect with the MichelsoninterferometerLI 6 (P1307100)Magnetostriction with the MichelsoninterferometerLI 10 (P1307500)Determination of the refraction index ofair with the Mach-Zehnder interfero-meter

LI 12 (P1307700)Fabry-Perot interferometer – Determina-tion of the laser light’s wavelengthLI 13 (P1307800)Fabry-Perot interferometer – optical resonator modes

LI 15 (P2261200)Fourier optics – optical filtration – 4f ArrangementLI 17 (P1308000)LDA – Laser Doppler Anemometry

For free

LEP_2 09.08.2007 11:48 Uhr Seite 123


Optics Handbooks

1 Propagation of light

OT 1.1 (11000)Rectilinear propagation of lightOT 1.2 (11001)Shadow formation by a point light sour-ceOT 1.3 (11002)Umbra and penumbra with two pointlight sourcesOT 1.4 (11003)Umbra and penumbra with an extensivelight sourceOT 1.5 (11004)Length of shadowsOT 1.6 (11005)Solar and lunar eclipses with a pointlight sourceOT 1.7 (11006)Solar and lunar eclipses with anextensive light source

2 Mirrors

OT 2.1 (11007)Reflection of lightOT 2.2 (11008)The law of reflectionOT 2.3 (11009)Formation of an image point by a planemirrorOT 2.4 (11010)Image formation by a plane mirrorOT 2.5 (11011)Applications of reflection by plane mir-rorsOT 2.6 (11012)Reflection of light by a concave mirrorOT 2.7 (11013)Properties of a concave mirrorOT 2.8 (11014)Real images with a concave mirrorOT 2.9 (11015)Law of imagery and magnification of aconcave mirrorOT 2.10 (11016)Virtual images with a concave mirrorOT 2.11 (11017)Aberrations with a concave mirrorOT 2.12 (11018)Reflection of light by a convex mirror

OT 2.13 (11019)Properties of a convex mirrorOT 2.14 (11020)Image formation by a convex mirrorOT 2.15 (11021)Law of imagery and magnification of aconvex mirrorOT 2.16 (11022)Reflection of light by a parabolic mirror

3 Refraction

OT 3.1 (11023)Refraction at the air-glass boundaryOT 3.2 (11024)Refraction at the air-water boundaryOT 3.3 (11025)The law of refractionOT 3.4 (11026)Total reflection at the glass-air boundaryOT 3.5 (11027)Total reflection at the water-airboundaryOT 3.6 (11028)Passage of light through a planoparallelglass plateOT 3.7 (11029)Refraction by a prismOT 3.8 (11030)Light path through a reversing prismOT 3.9 (11031)Light path through a deflection prismOT 3.10 (11032)Light transmission by total reflection

4 Lenses

OT 4.1 (11033)Refraction of light by a convergent lensOT 4.2 (11034)Properties of a convergent lensOT 4.3 (11035)Real images with a convergent lensOT 4.4 (11036)Law of imagery and magnification of aconvergent lensOT 4.5 (11037)Virtual images with a convergent lensOT 4.6 (11038)Refraction of light at a divergent lensOT 4.7 (11039)Properties of a divergent lens

OT 4.8 (11040)Image formation by a divergent lensOT 4.9 (11041)Law of imagery and magnification of adivergent lensOT 4.10 (11042)Lens combination consisting of two convergent lensesOT 4.11 (11043)Lens combination consisting of aconvergent and a divergent lensOT 4.12 (11044)Spherical aberrationOT 4.13 (11045)Chromatic aberration

5 Colours

OT 5.1 (11046)Colour dispersion with a prismOT 5.2 (11047)Non-dispersivity of spectral coloursOT 5.3 (11048)Reunification of spectral coloursOT 5.4 (11049)Complementary colours

OT 5.5 (11050)Additive colour mixingOT 5.6 (11051)Subtractive colour mixing

6 The human eye

OT 6.1 (11052)Structure and function of the human eyeOT 6.2 (11053)Short-sightedness and its correctionOT 6.3 (11054)Long-sightedness and its correction

7 Optical equipment

OT 7.1 (11055)The magnifying glassOT 7.1 (11056)The cameraOT 7.3 (11057)The astronomical telescopeOT 7.4 (11058)The Newtonian reflecting telescopeOT 7.5 (11059)Herschel’s reflecting telescope


PHYSICS

Magnet Board Optics

0115

1.02

Georg Schollmeyer

Geometrical optics and theory of colours on the magnetic boardThe demonstration system presents the following advantages:

● simple handling and minimum preparation time through components with magnets

● clear length of beams through 50 W halogen lamp with magnet and large model objects

● clear and dust proof storage of all components in the device shapedwooden tray

● detailed description of experiments with figures.60 experiments covering light propagation (7), mirror (16), diffraction (10), lenses (13),colours (6), eye (3), optical instruments (5)


Physics Demonstration Experiments – Magnet Board Optics • No. 01151.02 • 60 described ExperimentsPlease ask for a complete equipment list Ref. No. 22701

Light guide

LEP_2 09.08.2007 11:48 Uhr Seite 124

3Thermodynamics

LEP_3 09.08.2007 11:50 Uhr Seite 125


Contents

3.1 Thermal Expansion

3.1.01-00 Thermal expansion in solids and liquids

3.2 Ideal and Real Gases


3.2.01-15 Equation of state of ideal gases with Cobra3


3.2.02-11 Heat capacity of gases with Cobra3


3.2.04-00 Thermal equation of state and critical point


3.2.06.00 Joule-Thomson effect

3.3 Calorimetry, Friction Heat


3.3.01-11 Heat capacity of metals with Cobra3


Thermodynamics

3.4 Phase Transitions

3.4.01-00 Vapour pressure of water at high temperature

3.4.02-00 Vapour pressure of water below 100°C / Molar heat of vaporization

3.4.03-00 Boiling point elevation


3.5 Transport and Diffusion

3.5.01-01/15 Stefan-Boltzmann’s law of radiation


3.6 Applied Thermodynamics

3.6.01-00 Solar ray Collector

3.6.02-00 Heat pump

3.603-00 Heat insulation / Heat conduction


3.7 Handbooks

Glas jacket system

Demonstration Experiments Physics – Magnetic Board Heat

3LEP_3 09.08.2007 11:50 Uhr Seite 126


Thermal expansion in solids and liquids 3.1.01-00

Thermal Expansion Thermodynamics

Principle:The volume expansion of liquids andthe linear expansion of various ma-terials is determined as a function oftemperature.

Tasks:1. To determine the volume expan-

sion of ethyl acetate (C4H8O2),methylated spirit, olive oil, glyceroland water as a function of temper-ature, using the pycnometer.

2. To determine the linear expansionof brass, iron, copper, aluminium,

Relationship between length l and temperature �, for a) aluminium, b) brass,c) copper, d) steel, e) duran glass, f) quartz glass (lo = 600 mm)

duran glass and quartz glass as afunction of temperature using adilatometer.

3. To investigate the relationship be-tween change in length and over-all length in the case of alumini-um.


� Linear expansion� Volume expansion of liquids� Thermal capacity� Lattice potential� Equilibrium spacing� Grüneisen equation

Dilatometer with clock gauge for practical class experiments 04233.00 1

Tube for dilatometer, copper 04231.05 1

Tube for dilatometer, aluminium 04231.06 1

Tube for dilatometer, quarz glass 04231.07 1






Syringe 1 ml, Luer, pack of 10 02593.03 1

Cannula, LUER, d = 0.60 mm, 20 pcs. 02599.04 1

Measuring tube, l = 300 mm, IGJ 19/26 03024.00 2


Flat bottom flasks, DURAN®, 100 ml, IGJ 19/26 35811.01 2


Ethyl acetate, 250 ml 30075.25 1

Glycerol, 250 ml 30084.25 1

Olive oil, pure, 100 ml 30177.10 1

Precision Balance, Sartorius CP323P 48800.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedThermal expansion in solids and liquids P2310100

LEP_3 09.08.2007 11:50 Uhr Seite 127



Principle:The state of a gas is determined byits temperature, its pressure and theamount of substance. For the limit-ing case of an ideal gas these statevariables are linked by the generalequation of state, from which specialcorrelations can be derived for spe-cific changes of state.

Tasks:For a constant amount of gas (air)investigate the correlation of

1. Volume and pressure at constanttemperature (Boyle and Mariotte’slaw)

2. Volume and temperature at con-stant pressure (Gay-Lussac’s law)

3. Pressue and temperature at con-stant volume (Charles’ (Amontons’law))

Correlation between pressure p and volume V for a constant quantity of air(n = 0.9536 mmol) during an isothermic change of state (T = 298.15 K).

From the relationships obtained cal-culate the universal gas constant aswell as the coefficient of thermal ex-pansion, the coefficient of thermaltension, and the coefficient of cubiccompressibility.

Gas law apparatus 04362.00 1




Weather monitor, 6 lines LCD 87997.10 1


Mercury tray 02085.00 1





Pinchcock, width 15 mm 43631.15 1

Hose clip, d = 8-12 mm 40996.01 6


Mercury, filtered, 1000 g 31776.70 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedEquation of state of ideal gases P2320101

Thermodynamics Ideal and Real Gases


� Pressure and temperature� Volume� Coefficient of thermal

expansion� Coefficient of thermal

tension� Coefficient of cubic

compressibility� General equation of state for

ideal gases� Universal gas constant� Boyle and Mariotte’s law� Gay-Lussac’s law� Charles’ (Amontons’) law

LEP_3 09.08.2007 11:50 Uhr Seite 128


Equation of state of ideal gases with Cobra3 3.2.01-15

Ideal and Real Gases Thermodynamics

Principle:The state of a gas is determined bytemperature, pressure and amount ofsubstance. For the limiting case ofideal gases, these state variables arelinked via the general equation ofstate. For a change of state underisochoric conditions this equationbecomes Amontons’ law.

In this experiment it is investigatedwhether Amontons’ law is valid for aconstant amount of gas (air).

Dependence of the pressure on the temperature under isochoric conditions.


� Thermal tension coefficient� General equation of state

for ideal gases� Universal gas constant� Amontons’ law




Measuring module pressure 12103.00 1

Measuring module temperature NiCr-Ni, 330°C 12104.00 1

Thermocouple NiCr-Ni, sheathed 13615.01 1

Cobra3 measuring module converter 12150.04 1

Temperature sensor, semiconductor type 12120.00 1

Software Cobra3 Gas Laws 14516.61 1

Glass jacket 02615.00 1

Gas syringes, without cock, 100 ml 02614.00 1

Heating apparatus 32246.93 1

Power regulator 32288.93 1

H-base -PASS- 02009.55 1





Magnet rod, l = 200 mm, d = 10 mm 06311.00 1

Magnetic stirring rod, cylindrical, l = 30 mm 46299.02 1


Funnel, glass, d = 50 mm 34457.00 1

Hose connector, reducing, d = 3-5/6-10 mm 47517.01 1

Silicone tubing, d = 2 mm 39298.00 1

Silicone tubing, d = 7 mm 39296.00 1

Hose clip, d = 8-12 mm 40996.01 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedEquation of state of ideal gaseswith Cobra3 P2320115

Tasks:For a constant amount of gas (air)investigate the correlation of

1. Volume and pressure at constanttemperature (Boyle and Mariotte’slaw)

2. Volume and temperature at con-stant pressure (Gay-Lussac’s law)

3. Pressue and temperature at con-stant volume (Charles’ (Amontons’law))

From the relationships obtained cal-culate the universal gas constant aswell as the coefficient of thermal ex-pansion, the coefficient of thermaltension, and the coefficient of cubiccompressibility.

LEP_3 09.08.2007 11:51 Uhr Seite 129




Principle:Heat is added to a gas in a glass ves-sel by an electric heater which isswitched on briefly. The temperatureincrease results in a pressureincrease, which is measured with amanometer. Under isobaric condi-tions a temperature increase resultsin a volume dilatation, which can beread from a gas syringe. The molarheat capacities CV and Cp are calcu-lated from the pressure or volumechange.

Pressure change �p as a function of the heat-up time �t. U = 4.59 V, I = 0.43 A

Tasks:Determine the molar heat capacitiesof air at constant volume CV and atconstant pressure Cp.


� Equation of state for idealgases

� 1st law of thermodynamics� Universal gas constant� Degree of freedom� Mole volumes� Isobars� Isotherms� Isochors and adiabatic

changes of slate


Hand held measuring instrument Pressure, RS 232 07136.00 1



Mariotte flask, 10 l 02629.00 1


Glass stopcocks, 1 way, straight 36705.00 1

Three-way cock 36732.00 1

Rubber stopper, d = 32/2 6mm, 3 holes 39258.14 1

Rubber stopper, d = 59.5/50.5 mm, 1 hole 39268.01 1


Nickel electrode with socket, d = 3 45231.00 2

Nickel electrode 45218.00 1

Chrome-nickel wire, d = 0.1 mm, l = 100 m 06109.00 1

Scissors, stainless, l = 140 mm, round 64625.00 1

Push button switch, circuit closing 06039.00 1


Carbon resistor 1 kΩ, 1 W, G1 39104.19 1

Capacitor 2000 nF/ 250 V, G2 39105.29 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat capacity of gases P2320201

LEP_3 09.08.2007 11:51 Uhr Seite 130



Heat capacity of gases with Cobra3 3.2.02-11

Principle:Heat is added to a gas in a glass ves-sel by an electric heater which isswitched on briefly. The temperatureincrease results in a pressureincrease, which is measured with amanometer. Under isobaric condi-tions a temperature increase resultsin a volume dilatation, which can beread from a gas syringe. The molarheat capacities CV and Cp are calcu-lated from the pressure or volumechange.

Volume change �V as a function of the heat-up time �t. U = 4.59 V, I = 0.43 A.

Tasks:Determine the molar heat capacitiesof air at constant volume CV and atconstant pressure Cp.






Cobra3 current probe 6 A 12126.00 1

Mariotte flask, 10 l 02629.00 1


Glass stopcocks, 1 way, straight 36705.00 1

Three-way cock 36732.00 1

Rubber stopper, d = 32/26 mm, 3 holes 39258.14 1

Rubber stopper, d = 59.5/50.5 mm, 1 hole 39268.01 1


Nickel electrode with socket, d = 3 45231.00 2

Nickel electrode 45218.00 1

Chrome-nickel wire, d = 0.1 mm, l = 100 m 06109.00 1

Scissors, stainless, l = 140 mm, round 64625.00 1

Push button switch, circuit closing 06039.00 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat capacity of gases with Cobra3 P2320211


� Equation of state for idealgases

� 1st law of thermodynamics� Universal gas constant

Degree of freedom� Mole volumes� Isobars� Isotherms� Isochors and adiabatic

changes of slate

LEP_3 09.08.2007 11:51 Uhr Seite 131




Principle:By means of the model apparatus forkinetic theory of gases the motion ofgas molecules is simulated and thevelocity is determined by registrationof the throw distance of the glassballs. This velocity distribution iscompared to the theoretical MAX-WELL-BOLTZMANN equation.

Experimental and theoretical velocity distribution in the model experiment.

Tasks:1. Measure the velocity distribution

of the “model gas”.

2. Compare the result to theoreticalbehaviour as described by theMAXWELL-BOLTZMANN distribu-tion.

3. Discuss the results.


� Kinetic theory of gases� Temperature� Gas� Molecules� Model kinetic energy� Average velocity� Velocity distribution

Kinetic gas theory apparatus 09060.00 1

Receiver with recording chamber 09061.00 1







Test tube, AR-glass, d = 16 mm 37656.10 1

Test tube rack for 12 tubes, wood 37686.10 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMaxwellian velocity distribution P2320300

LEP_3 09.08.2007 11:51 Uhr Seite 132



Thermal equation of state and critical point 3.2.04-00

Principle:A substance which is gaseous undernormal conditions is enclosed in avariable volume and the variation ofpressure with the volume is recordedat different temperatures. The criti-cal point is determined graphicallyfrom a plot of the isotherms.

p-V-isotherms of ethane.

Tasks:1. Measure a number of p-V-iso-

therms of ethane.

2. Determine the critical point andthe critical quantities of ethane.

3. Calculate the constants of theVan der WAALS equation, theBOYLE-temperature, the radius ofthe molecules and the parametersof the interaction potential.

Critical point apparatus 04364.10 1




Gasket for GL18, hole d = 8 mm, 10 pcs 41240.03 1

Vacuum pump, rotary sliding-vane, one-stage 02750.93 1

Adapter 02657.00 1

Safety bottle, 500 ml, 2 x Gl18/8, 1 x 25/12 34170.88 1






Rubber tubing, d = 8 mm 39283.00 4

Rubber tubing, vacuum, i.d. = 8 mm 39288.00 1

Rubber tubing/vacuum, d = 6 mm 39286.00 1


Hose clip, d = 8-12 mm 40996.01 4

Hose clip for 12-20 diameter tube 40995.00 2

Mercury tray 02085.00 1

Compressed gas, ethane, 14 g 41772.09 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedThermal equation of state and critical point P2320400


� Ideal gas� Real gas� Equation of state� Van der WAALS equation� BOYLE temperature� Critical point� Interaction potential� Molecule radius

LEP_3 09.08.2007 11:51 Uhr Seite 133




Principle:A mass oscillates on a volume of gasin a precision glass tube. The oscilla-tion is maintained by leading escap-ing gas back into the system. Theadiabatic coefficient of various gasesis determined from the periodic timeof the oscillation.

Tasks:

Determine the adiabatic coefficient� of air nitrogen and carbon dioxide(and also of argon, if available) fromthe periodic time of the oscillation Tof the mass m on the volume V ofgas


� Equation of adiabatic changeof slate

� Polytropic equation� Rüchardt’s experiment� Thermal capacity of gases

Gas oscillator, Flammersfeld 04368.00 1

Graduated cylinder, BORO 3.3, 1000 ml 36632.00 1

Aspirator bottle, clear glass, 1000 ml 34175.00 1

Air control valve 37003.00 1



Micrometer 03012.00 1

Glass tube, AR-glass, right-angled, l = 85 + 60 mm, 10 pcs. 36701.52 1

Rubber stopper, d = 22/17 mm, 1 hole 39255.01 1

Rubber stopper, d = 32/26 mm, 1 hole 39258.01 1


Sliding weight balance, 101 g 44012.01 1

Aquarium pump, 230 V AC 64565.93 1

Aneroid barometer 03097.00 1

Stopwatch, 15 minutes 03076.01 1





Pressure-reducing valves, CO2 / He 33481.00 1

Pressure-reducing valves, nitrogen 33483.00 1

Steel cylinders, carbon dioxide, 10 l 41761.00 1

Steel cylinders, nitrogen, 10 l 41763.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedAdiabatic coefficient of gases –Flammersfeld oscillator P2320500

Ten measurements, each of about n = 300 oscillations, gave for theadiabatic coefficients

Argon � = 1.62 ± 0.09

Nitrogen � = 1.39 ± 0.07

Carbon dioxide � = 1.28 ± 0.08

Air � = 1.38 ± 0.08

LEP_3 09.08.2007 11:51 Uhr Seite 134



Joule-Thomson effect 3.2.06.00

Principle:A stream of gas is fed to a throttlingpoint, where the gas (CO2 or N2) un-dergoes adiabatic expansion. The dif-ferences in temperature establishedbetween the two sides of the throt-tle point are measured at variouspressures and the Joule-Thomsoncoefficients of the gases in questionare calculated.

Temperature differences measured at various ram pressures.

Tasks:1. Determination of the Joule-Thom-

son coefficient of CO2.

2. Determination of the Joule-Thom-son coefficient of N2.

Joule-Thomson apparatus 04361.00 1

Temperature meter digital, 4-2 13617.93 1

Temperature probe, Pt100 11759.01 2

Pressure-reducing valves, CO2 / He 33481.00 1

Pressure-reducing valves, nitrogen 33483.00 1

Wrench for steel cylinders 40322.00 1

Steel cylinder, nitrogen, 10 l 41763.00 1

Steel cylinder, CO2, 10 l 41761.00 1

Gas-cylinder Trolley for 2 Cylinder 41790.20 1

Hose clip for 12-20 diameter tube 40995.00 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedJoule-Thomson effect P2320600


� Real gas� Intrinsic energy� Gay-Lussac theory� Throttling� Van der Waals equation� Van der Waals force� Inverse Joule-Thomson effect� Inversion temperature

LEP_3 09.08.2007 11:51 Uhr Seite 135


Thermodynamics Calorimetry, Friction Heat


Principle:Heated specimens are placed in acalorimeter filled with water at lowtemperature. The heat capacity ofthe specimen is determined from therise in the temperature of the water.

Temperature as a function of time in the method of mixtures experiment a) steel, b) brass, c) aluminium.

Tasks:1. To determine the heat capacity of

the calorimeter by filling it withhot water and determining therise in temperature.


� Mixture temperature� Boiling point� Dulong Petit’s law� Lattice vibration� Internal energy� Debye temperature

Calorimeter, 500 ml 04401.00 1

Metal bodies, set of 3 04406.00 4

Steel pot, 1 l 05933.00 1

Butane burner Labogaz 206 32178.00 1

Butane cartridge C 206 without valve 47535.00 1

Aneroid barometer 03097.00 1

Precision mercury thermometers, -10...+ 50°C 38033.00 1


Portable Balance, OHAUS JR300 48891.00 1


Wire triangle (clay triangle), l = 60 mm 33278.00 1

Tripod, ring d = 140 mm, h = 240 mm 33302.00 1



Glass beads, 850 pieces, d = 6 mm 36756.25 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat capacity of metals P2330101

2. To determine the specific heatcapacity of aluminium, iron andbrass.

3. To verify Dulong Petit’s law withthe results of these experiments.

LEP_3 09.08.2007 11:51 Uhr Seite 136


Calorimetry, Friction Heat Thermodynamics

Heat capacity of metals with Cobra3 3.3.01-11

Principle:Heated specimens are placed in acalorimeter filled with water at lowtemperature. The heat capacity ofthe specimen is determined from therise in the temperature of the water.

Course of temperature in the calorimeter.For 180 g Iron (100 °C) and 200 g water (room-temperature).

Tasks:1. To determine the specific heat

capacity of aluminium, iron andbrass.

2. To verify Dulong Petit’s law withthe results of these experiments.



Software Cobra3 Temperature 14503.61 1

Measuring module temperature NiCr-Ni, 330°C 12104.00 1

Immersion probe NiCr-Ni,-50/1000°C 13615.03 1

H-base -PASS- 02009.55 1


Bosshead 02043.00 2


Ring with Bosshead, i.d. = 10 cm 37701.01 1

Wire nets, 160 x 160 mm 33287.01 1

Metal bodies, set of 3 04406.00 3




Portable Balance, OHAUS JR300 48891.00 1


Calorimeter vessel, 500 ml 04401.10 1



Stirring rod 04404.10 1

Pipette, with rubber bulb 64701.00 1

Beads, 200 g 36937.20 1


Paper tissues

What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat capacity of metals with Cobra3 P2330111


� Mixture temperature� Boiling point� Dulong Petit’s law� Lattice vibration� Internal energy� Debye temperature

LEP_3 09.08.2007 11:51 Uhr Seite 137


Thermodynamics Calorimetry, Friction Heat


�T

A1

A2

T2

28

27

26

25

24

T°C

X

XXX X

XXXX

X

120 240 360 480 600 7200

XX

X

X

X X X X X X X X XT1

ts

Principle:In this experiment, a metal test bodyis rotated and heated by the frictiondue to a tensed band of syntheticmaterial. The mechanical equivalentof heat for problem 1 is determinedfrom the defined mechanical workand from the thermal energyincrease deduced from the increaseof temperature. Assuming the equiv-alence of mechanical work and heat,the specific thermal capacity of alu-minum and brass is determined.

Temperature-time diagram for a measurement example.

Tasks:1. Determination of the mechanical

equivalent of heat.

2. Determination of the specificthermal capacity of aluminum andbrass.


� Mechanical equivalent of heat� Mechanical work� Thermal energy� Thermal capacity� First law of thermodynamics� Specific thermal capacity

Mechanical equivalence of heat apparatus 04440.00 1

Friction cylinder CuZn, 1.28 kg 04441.02 1

Friction cylinder Al, 0.39 kg 04441.03 1








Commercial weight, 1000 g 44096.70 1

Commercial weight, 5000 g 44096.81 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMechanical equivalent of heat P2330200

LEP_3 09.08.2007 11:51 Uhr Seite 138


Phase Transitions Thermodynamics

Vapour pressure of water at high temperature 3.4.01-00

Principle:Water is heated in a closed pressurechamber; as much water vaporises asto make the pressure in the chambercorrespond to the vapour pressure atthe temperature at any time. Theheat of vaporisation is determined atvarious temperatures from the meas-urement of vapour pressure as afunction of temperature.

Natural logarithm of vapour pressure p as a function of the reciprocal of thetemperature (1/T): Tb = boiling point at normal pressure.

Tasks:1. To measure the vapour pressure of

water as a function of tempera-ture.

2. To calculate the heat of vaporisa-tion at various temperatures fromthe values measured.

3. To determine boiling point at nor-mal pressure by extrapolation.

High pressure vapour unit 02622.10 1

Heat conductive paste, 50 g 03747.00 1

Heating apparatus 32246.93 1

Pipette, with rubber bulb, long 64821.00 1


Bosshead 02043.00 1


Laboratory thermometer, -10...+250°C 38065.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedVapour pressure of water at hightemperature P2340100


� Boiling point� Heat of vaporisation� Clausius-Clapeyron equation� Van’t Hoff law� Carnot cycle

LEP_3 09.08.2007 11:51 Uhr Seite 139


Thermodynamics Phase Transitions

3.4.02-00 Vapour pressure of water below 100°C – Molar heat of vaporization

Principle:The vapour pressure of water in therange of 40°C to 85°C is investigat-ed. It is shown that the Clausius-Clapeyron equation describes the re-lation between temperature andpressure in an adequate manner. Anaverage value for the heat of vapor-ization of water is determined.

Tasks:1. About 250 ml of de-mineralized

water are allowed to boil forabout 10 minutes to eliminate alltraces of dissolved gas. The wateris then cooled down to room tem-perature.

2. The 3-neck round flask is filledabout three-quarters full with

Semilogarithmic representation of vapour pressure p as a function of 1/T.

gas-free water and heated. At 35°Cthe space above the water within theround flask is evacuated. Furtherheating causes an increase in pressure p and temperature t ofwater within the round flask. p and tare read in steps of 5 °C up to a max-imum of t = 85°C.

Manometer -1.0...0.6 bar 03105.00 1

Thermometer, -10...+110 °C 38005.02 2

Round flask, 100 ml, 3 necks, GL25, 2 x GL18 35677.15 1

Glass stopcocks, 1 way, right-angled 36705.01 1

Vacuum pump, rotary sliding-vane, one-stage 02750.93 1

Magnetic stirrer, Heating, Temperature-connection, 10 l 35731.93 1


Glass tube 200 mm ext. d = 8 mm 64807.00 1

Gasket for GL 18, 8 mm hole, 10 pcs 41242.03 1





Support rod with hole, stainless steel, l = 50 cm, M10 thread 02022.20 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedVapour pressure of water below 100°C – Molar heat of vaporization P2340200


� Pressure� Temperature� Volume� Vaporization� Vapour pressure� Clausius-Clapeyron equation

LEP_3 09.08.2007 11:51 Uhr Seite 140


Boiling point elevation 3.4.03-00

Phase Transitions Thermodynamics

Principle:The boiling point of a solution isalways higher than that of the puresolvent. The dependence of the tem-perature difference (elevated boilingpoint) on the concentration of thesolute can be determined using asuitable apparatus.

Example of a measurement: boiling point increase as function of concentra-tion of table salt in an aqueous solution.

Tasks:1. Measure the increase in boiling

point of water as a function of theconcentration of table salt, ureaand hydroquinone.

2. Investigate the relationshipbetween the increase in boilingpoint and the number of particles.

3. Determine the molar mass of thesolute from the relationshipbetween the increase in boilingpoint and the concentration.


� Raoult’s law� Henry’s law� Ebullioscopic constants� Chemical potential� Gibbs-Helmholtz equation� Concentration ratio� Degree of dissociation

Appartus for elevation of boiling point 36820.00 1Heating mantle for roundbottom flask, 250 ml 49550.93 1Clamp for heating mantle 49557.01 1Power regulator 32288.93 1Precision Balance, Sartorius LE 623P 48852.93 1Weighing dishes, square shape, 84 x 84 x 24 mm, 25 pcs. 45019.25 1Temperature meter digital, 4-2 13617.93 1Temperature probe, Pt100 11759.01 1Protective sleeves for temperature probe, 2 pcs. 11762.05 1Retort stand, h = 750 mm 37694.00 1Right angle clamp 37697.00 3Universal clamp 37718.00 3Flask, round, 1 neck, 250 ml, GL25/14 35812.15 1Beaker, DURAN®, tall form, 250 ml 36004.00 1Gasket for GL 18, 8 mm hole, 10 pcs 41242.03 1Silicone tubing, d = 7 mm 39296.00 1Mortar with pestle, 150 ml, porcelain 32604.00 3Pinchcock, width 15 mm 43631.15 1Spoon with spatula end, l = 150 mm, steel, micro 33393.00 1Wash bottle, plastic, 500 ml 33931.00 1Pellet press for calorimeter 04403.04 1Funnel, glass, d = 80 mm 34459.00 1Pasteur pipettes, l = 145 ml 36590.00 1Rubber caps, 10 pcs 39275.03 1Beads, 200 g 36937.20 1Sodium chloride, 500 g 30155.50 1Urea, 250 g 30086.25 1Hydroquinone, 250 g 30089.25 1Glycerol, 250 ml 30084.25 1Water, distilled 5 l 31246.81 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedBoiling point elevation P2340300

LEP_3 09.08.2007 11:51 Uhr Seite 141


Thermodynamics Phase Transitions


Principle:The freezing point of a solution islower than that of the pure solvent.The depression of the freezing pointcan be determined experimentallyusing a suitable apparatus (cryosco-py). If the cryoscopic constants ofthe solvent are known, the molecularmass of the dissolved substances canbe determined.

Cooling curve of water/table salt (NaCI) mixture.

Tasks:1. Determine the size of freezing

point depression after dissolving astrong electrolyte (NaCI) in water.By comparing the experimentalvalue with the theoretical onepredicted for this concentration,determine the number of ions intowhich the electrolyte dissociates.

2. Determine the apparent molarmass of a non-electrolyte (hydro-quinone) from the value of freez-ing point depression.

Apparatus for freezing point depression 36821.00 1

Gaskets for connecting caps, GL 25 41243.03 1

Temperature meter digital, 4-2 13617.93 1

Temperature probe, Pt100 11759.01 2

Protective sleeves for temperature probe, 2 pcs. 11762.05 1

Pellet press for calorimeter 04403.04 1

Magnetic stirrer mini, plastic (ABS) 47334.93 1




Volumetric pipettes, 50 ml 36581.00 1

Safety pipettor Flip 36592.00 1

Retort stand, h = 1000 mm 37695.00 1



Precision Balance, Sartorius TE 153S 48832.93 1


Mortar with pestle, 70 ml, porcelain 32603.00 2

Spoon with spatula end, l = 150 mm, steel, micro 33393.00 1

Spoon with spatula end, l = 150 mm, steel, wide 33398.00 1

Funnel, plastic, d = 50 mm 36890.00 1

Weighing dishes, square shape, 84 x 84 x 24 mm, 25 pcs. 45019.25 1

Pasteur pipettes, l = 145 ml 36590.00 1

Rubber caps, 10 pcs 39275.03 1



Hydroquinone, 250 g 30089.25 1

Denatured alcohol (Spirit forburning), 1000 ml 31150.70 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFreezing point depression P2340400


� Raoult’s law� Cryoscopic constants� Chemical potential� Gibbs-Helmholtz equation� Concentration ratio� Degree of dissociation� Van’t Hoff factor� Cryoscopy

LEP_3 09.08.2007 11:51 Uhr Seite 142


Stefan-Boltzmann’s law of radiation 3.5.01-01/15

Transport and Diffusion Thermodynamics

Principle:According of Stefan-Boltzmann’slaw, the energy emitted by a blackbody per unit area and unit time isproportional to the power “four” ofthe absolute temperature of thebody. Stefan-Boltzmann’s law is alsovalid for a so-called “grey” bodywhose surface shows a wavelength-independent absorption-coefficientof less than one. In the experiment,the “grey” body is represented by thefilament of an incandescent lampwhose energy emission is investigat-ed as a function of the temperature.

Thermoelectric e. m. f. of thermopile as a function of the filament’s absolutetemperature.

Tasks:1. To measure the resistance of the

filament of the incandescent lampat room temperature and to ascer-tain the filament’s resistance R0

at zero degrees centrigrade.

2. To measure the energy flux densityof the lamp at different heatingvoltages. The corresponding heat-ing currents read off for eachheating voltage and the corre-sponding filament resistance cal-culated. Anticipating a tempera-ture-dependency of the secondorder of the filament-resistance,the temperature can be calculatedfrom the measured resistances.


� Black body radiation� Thermoelectric e.m. f.� Temperature dependence of

resistances

Experiment P2350115 with Cobra3Experiment P2350101 with amplifier





Thermopile, Moll type 08479.00 1 1

Shielding tube for thermopile 08479.01 1 1

Variable transformer with rectifier 15 V~/12 V- , 5 A 13530.93 1 1

Lamp socket E 14, on stem 06175.00 1 1

Filament lamps, 6 V/5 A 06158.00 3 3

Connection box 06030.23 1 1

Resistor 100 Ω 2%, 1W, G1 06057.10 1 1

Digital multimeter 2010 07128.00 3 1




Meter Scale, l = 1000 x 27 mm 03001.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedStefan-Boltzmann’s law of radiation P2350101/15


LEP_3 09.08.2007 11:51 Uhr Seite 143

144 PHYWE Systeme GmbH & Co. KG · D-37070 Göttingen

Thermodynamics Transport and Diffusion

Laboratory Experiments Physics


Principle:The thermal conductivity of copperand aluminium is determined in aconstant temperature gradient fromthe calorimetrically measured heatflow.

The electrical conductivity of copperand aluminium is determined, andthe Wiedmann-Franz law is tested.

Multi-tap transformer with rectifier 14 VAC/12 VDC, 5 A 13533.93 1Digital multimeter 2010 07128.00 2Universal measuring amplifier 13626.93 1Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 4Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 4

Diagram: Heat of surroundings overtime.

Tasks:1. Determine the heat capacity of

the calorimeter in a mixtureexperiment as a preliminary test.Measure the calefaction of waterat a temperature of 0 °C in a calo-rimeter due to the action of theambient temperature as a func-tion of time.

2. To begin with, establish a constanttemperature gradient in a metalrod with the use of two heat res-ervoirs (boiling water and icewater) After removing the piecesof ice, measure the calefaction ofthe cold water as a function oftime and determine the thermalconductivity of the metal rod.

3. Determine the electrical conduc-tivity of copper and aluminium byrecording a current-voltage char-acteristic line.

4. Test of the Wiedmann-Franz law.

Calorimeter vessel, 500 ml 04401.10 1Calorimeter vessel with heat conductivity connection 04518.10 1Heat conductivity rod, Cu 04518.11 1Heat conductivity rod, Al 04518.12 1Magnetic stirrer mini, plastic (ABS) 47334.93 1Heat conductive paste, 50 g 03747.00 1Gauze bag 04408.00 1Rheostats, 10 Ω, 5.7 A 06110.02 1Immersion heater, 300 W, 220-250 VDC/AC 05947.93 1Temperature meter digital, 4-2 13617.93 1Temperature probe, Pt100 11759.01 1Temperature surface probe Pt 100 11759.02 2Stopwatch, digital, 1/100 s 03071.01 1Tripod base -PASS- 02002.55 1Bench clamp -PASS- 02010.00 1Support rod -PASS-, square, l = 630 mm 02027.55 1Support rod -PASS-, square, l = 1000 mm 02028.55 1Universal clamp 37718.00 4Right angle clamp -PASS- 02040.55 6Supporting block 105 x 105 x 57 mm 02073.00 1Beaker, DURAN®, short form, 400 ml 36014.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedThermal and electrical conductivity of metals P2350200


� Electrical conductivity� Wiedmann-Franz law� Lorenz number� Diffusion� Temperature gradient� Heat transport� Specific heat� Four-point measurement

For the electrical conductivity you need:

LEP_3 09.08.2007 11:51 Uhr Seite 144

145PHYWE Systeme GmbH & Co. KG · D-37070 Göttingen Laboratory Experiments, Physics

Solar ray Collector 3.6.01-00

Applied Thermodynamics Thermodynamics

Principle:The solar ray collector is illuminatedwith a halogen lamp of known lightintensity. The heat energy absorbedby the collector can be calculatedfrom the volume flow and the differ-ence in the water temperatures atthe inlet and outlet of the absorber,if the inlet temperature stays almostconstant by releasing energy to areservoir. The efficiency of the col-lector is determined from this. Themeasurement is made with variouscollector arrangements and at vari-ous absorber temperatures.

Tasks:To determine the efficiency of thesolar ray collector under various ex-perimental conditions.

1. Absorption of energy from the en-vironment (20°C) without illumi-nation by sun or halogen lamp,water temperature at the absorberinlet �e ≈ 5°C.

1.1 Absorber with insulation andglass plate (complete collec-tor)

1.2 Absorber alone(energy ceiling)

Water Temperatures and Collector Efficiency under VariousExperimental Conditions, m· = 100 cm3/min, qi = 1 kW/m2, A = 0 · 12 m2.

2. Illumination with halogen lamp.Water temperature qe≈ 20°C.

2.1 Complete collector

2.2 Collector without glass plate

3. Illumination with halogen lamp.Water temperature qe ≈ 50°C.

3.1 Complete collector

3.2 Complete collector, cold jet ofair impinges

3.3 Collector without glass plate

3.4 Collector without glass plate,cold jet of air impinges.


� Absorption� Heat radiation� Greenhouse effect� Convection� Conduction of heat� Collector equations� Efficiency� Energy ceiling

Solar collector 06753.00 1


Laboratory thermometer -10...+110 °C 38060.00 1

Circulating pump w. flowmeter 06754.01 1


Heat exchanger 06755.00 1

Stand for solar collector 06757.00 1

Immersion heater, 1000 W, 220-250 V 04020.93 1

Halogen lamp 1000 W 08125.93 1

Hot/cold air blower, 1700 W 04030.93 1







Safety gas tubing, DVGW, l = 1000 mm 39281.10 3





What you need:

Complete Equipment Set, Manual on CD-ROM includedSolar ray Collector P2360100

No. Glass Light Cold �plate air 0C K %

1.1 +* – – ≈ 5 2.5 15

1.2 –* – – ≈ 5 5.0 29

2.1 + + – ≈ 20 11.0 64

2.2 – + – ≈ 20 12.5 73

3.1 + + – ≈ 50 8.0 47

3.2 – + + ≈ 50 8.0 47

3.3 + + – ≈ 50 6.0 35

3.4 – + + ≈ 50 3.0 17

* This series of measurements without rear insulation

�a – �e�e

LEP_3 09.08.2007 11:51 Uhr Seite 145


Thermodynamics Applied Thermodynamics

3.6.02-00 Heat pump

�°C

60

50

40

30

20

10

0

-10

10 20 30 tmin�Vi

�2

�V0

�c0

�1

�ci

Principle:Pressures and temperatures in thecirculation of the heat electricalcompression heat pump are mea-sured as a function of time when it isoperated as a water-water heatpump.

The energy taken up and released iscalculated from the heating andcooling of the two water baths.

When it is operated as an air-waterheat pump, the coefficient of perfor-mance at different vaporiser temper-atures is determined.

Tasks:1. Water heat pump:

To measure pressure and tempera-ture in the circuit and in the waterreservoirs on the condenser sideand the vaporiser side alternately.To calculate energy taken up andreleased, also the volume concen-tration in the circuit and the volu-metric efficiency of the compres-sor.

2. Air-water heat pump:To measure vaporiser temperatureand water bath temperature on

Temperatures at the inlet and outlet of the vaporiser �Vi (�), �Vo (�) andcondenser �Ci (�), �Co (�) as a function of the operating time; continuouscurves: temperature in water reservoirs.

the condenser side under differentoperating conditions on the va-poriser side,

2.1 with stream of cold air

2.2 with stream of hot air

2.3 without blower.

If a power meter is available, theelectric power consumed by thecompressor can be determined withit and the coefficient of performancecalculated.

Heat pump, compressor principle 04370.88 1


Laboratory thermometer -10...+110 °C 38060.00 2










Option:

Work and power meter 13715.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat pump P2360200


� Refrigerator� Compressor� Restrictor valve� Cycle� Vaporization� Condensation� Vapour pressure� Vaporisation enthalpy

LEP_3 09.08.2007 11:51 Uhr Seite 146


Heat insulation / Heat conduction 3.6.03-00

Applied Thermodynamics Thermodynamics

Principle:A model house with replaceable sidewalls is used for determining theheat transition coefficients (k val-ues) of various walls and windowsand for establishing the heat con-ductivities of different materials. Forthis purpose the temperatures on theinside and outside of the walls aremeasured at a constant interior andouter air temperature (in the steadystate).

With a multilayer wall structure thetemperature difference over a layeris proportional to the particular ther-

mal transmission resistance. Thethermal capacity of the wall materi-al affects the wall temperatures dur-ing heating up and temporary expo-sure to solar radiation.

Heat transition resistance 1/k as a function of the wall thickness d.

Tasks:1. Measurement and interpretation

of water temperatures during theheating up and during temporaryexternal illumination of the walls.

2. Determination of the heat con-ductivities of wood and Styropor.

3. Determination of the k values ofordinary glass and insulating glasswindows and of wooden walls ofdifferent thicknesses, and of wallswith wood, Styropor or cavitylayers.


� Heat transition� Heat transfer� Heat conductivity� Thermal radiation� Hothouse effect� Thermal capacity� Temperature amplitude

attenuation

High insulation house 04507.93 1

Thermal regulation for high insulation house 04506.93 1

Partitions, plastic foam, 5 off 44536.02 1

Ceramic lamp socket E27 with reflector, switch, safety plug 06751.01 1

Filament lamp with reflector, 230 V/120 W 06759.93 1

Hand held instrument 2 x NiCr-Ni, RS 232 07140.00 2

Thermocouple NiCr-Ni, max. 500°C, simple 13615.02 4





What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat insulation / Heat conduction P2360300

LEP_3 09.08.2007 11:51 Uhr Seite 147


Thermodynamics Applied Thermodynamics


Principle:The Stirling engine is submitted to aload by means of an adjustabletorque meter, or by a coupled gener-ator. Rotation frequency and tem-perature changes of the Stirlingengine are observed. Effectivemechanical energy and power, aswell as effective electrical power, areassessed as a function of rotationfrequency. The amount of energyconverted to work per cycle can be

Tasks:1. Determination of the burner’s

thermal efficiency

2. Calibration of the sensor unit

3. Calculation of the total energyproduced by the engine throughdetermination of the cycle area onthe oscilloscope screen, usingtransparent paper and coordinatepaper.

Pressure as a function of Volume for the Stirling process.

4. Assessment of the mechanicalwork per revolution, and calcula-tion of the mechanical power out-put as a function of the rotationfrequency, with the assistance ofthe torque meter.

5. Assessment of the electric poweroutput as a function of the rota-tion frequency.

6. Efficiency assessment.

� First and second law of thermodynamics

� Reversible cycles� Isochoric and isothermal

changes� Gas laws� Efficiency� Stirling engine� Conversion of heat� Thermal pump

Experiment P2360415 with Cobra3Experiment P2360401 with oscilloscope

Stirling motor, transparent 04372.00 1 1Motor/Generator unit 04372.01 1 1Torque meter 04372.02 1 1Chimney for Stirling engine 04372.04 1 1Meter for Stirling engine, pVnT 04371.97 1 1Sensor unit pVn for Stirling engine 04371.00 1 1Syringe 20 ml, Luer, 10 pcs 02591.03 1Rheostats, 330 Ω, 1.0 A 06116.02 1Digital multimeter 2010 07128.00 2Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 2Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 3Oscilloscope 30 MHz, 2 channels 11459.95 1Screened cable, BNC, l = 750 mm 07542.11 2 2Thermocouple NiCr-Ni, sheathed 13615.01 2 2Cylinder, PP, 50 ml 36628.01 1Denatured alcohol (Spirit forburning), 1000 ml 31150.70 1 1Adapter BNC socket/4 mm plug pair 07542.27 2Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 1Software Cobra3 Universal recorder 14504.61 1PC, Windows® 95 or higherOptional accessories for solar motor workAccessories f. solar motor work 04372.03 1Support base -PASS- 02005.55 1Extension coupling, hinged 02045.00 1Support rod, stainl. steel, l = 500 mm 02032.00 1Optional accessories for heat pump workPower supply 13505.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedStirling engine P23604 01/15


determined with the assistance ofthe pV diagram. The efficiency of theStirling engine can be estimated.

LEP_3 09.08.2007 11:51 Uhr Seite 148


Handbooks Thermodynamics

GL 1 (12229)Gay-Lussac’s law

GL 2 (12230)Amonton’s law

GL 3 (12231)The Boyle-Mariotte law

GL 4 (12232)The gas laws of Boyle-Marriotte,Gay-Lussac and Amontons

GL 5 (12233)Determination of molar masses bymeans of vapour density method

GL6 (12234)The law of integral volumes

GL 7 (12235)Gay-Lussac’s law of gaseouscombustion

GL 8 (12236)Avogadro’s law

GL 9 (12237)The chemical formulafor methane, ethane and propane

GL 10 (12238)Determination of the heat offormation of water

GL 11 (12239)Determination of the heat offormation of CO2 and CO and Hess’slaw

GL 12 (12240)Determination of heating value (fuelvalue) of solid and gaseous fuels ina horizontal calorimeter

GL 13 (12241)Determination of the calorific valueof some foods

GL 14 (12242)Determination of the heating value(fuel value) of liquids in the verticalcalorimeter

GL 15 (12243)Determination of the fuel value ofheating oil and diesel fuel and thecalorific value of olive oil

GL 16 (12244)Chromatographic separation techni-ques: gas chromatography

GL 17 (12245)Distillation with steam

HANDBOOK

CHEMISTRY

Glass jacket system

0119

6.12

F. Lindenblatt / W. Jung

Glass jacket equipment systemThis system consists of a glass jacket, special inserts and accessories. It was mainlydeveloped for experiments with gases and can be used at school for teaching physics,chemistry and biology.● Demonstrative and transparent● Versatile and easily assembled● Water bath for accurate measurements

Fields of application:● Working out the laws of gases● Determination of molar masses● Determination of combustion enthalpies.

Glass jacket system

Glass jacket system • No. 01196.12 • 17 described ExperimentsPlease ask for a complete equipment list Ref. No. 23701

Amonton’s law (GL 2)

LEP_3 09.08.2007 11:51 Uhr Seite 149


Thermodynamics Handbooks

1 Thermal expansion1.1 (12913)Volume expansion of water

1.2 (12914)Preparing a thermometer scale

1.3 (12915)Linear expansion of solid bodies

1.4 (12916)Volume expansion of gases at constant pressure

1.5 (12917)Pressure elevation on heating gasesat constant volume

2 Heat transport2.1 (12918)Heat flux in liquids and gases

2.2 (12919)Heat conduction in solid bodies

2.3 (12920)Heat conduction in water

2.4 (12921)Absorption of thermal radiation

2.5 (12922)Utilisation of radiated energy with asolar collector

2.6 (12923)Utilisation of radiated energy with asolar cell

3 Refraction3.1 (12924)Gay-Lussac’s law

3.1 (12925)Charles’ law

3.3 (12926)Boyle and Mariotte’s law

3.4 (12927)Molar volume and universal gasconstant – Determination of therelative molar mass


PHYSICS

Magnetic Board Heat

0115

4.02

Regina Butt

The demonstration board with support stand finds application in all fields of physics. Experi-mentation on the board has the following advantages in the range of thermodynamics:● Quantity of liquids and convection currents in liquids can easily be seen in glass vessels

placed in front of the single-color background● Observations are supported by use of colored marking arrows and points● Description of the experiments and explanatory sketches and tables can be made directly

on the board● Individual positioning and simple movement of the holders● Secure positioning through strong magnets

Special holders and equipment allow a secure, simple and clear method of experimentation onthe demonstration board.The distance of the experimental equipment to the board are correlative and optimised for thespecified application.

Demonstration Experiments Physics– Magnetic Board Heat

Demonstration Experiments Physics – Magnetic Board Heat • No. 01154.02 • 15 described ExperimentsPlease ask for a complete equipment list Ref. No. 23703

Volume expansion of gases at constant pressure (1.4)

Linear expansion of solid bodies (1.3)

LEP_3 09.08.2007 11:51 Uhr Seite 150

4Electricity

LEP_4 09.08.2007 11:55 Uhr Seite 151


Contents

4.1 Stationary Currents

4.1.01-01 Measurement of small resistance


4.1.02-00 Wheatstone Bridge


4.1.04-01/15 Temperature dependence of different resistors and diodes

4.1.06-01/15 Current balance / Force acting on a current-carrying conductor

4.1.07-00 Semiconductor thermogenerator


4.1.09-01 Characteristic curves of a solar cell


4.1.11-00 Characteristic and efficiency of PEM fuel cell and PEM electrolyser


4.1.13-15 Second order conductors. Electrolysis with FG-Module

4.2 Electric Field


4.2.02-01 Charging curve of a capacitor


4.2.03-00 Capacitance of metal spheres and of a spherical capacitor


4.2.04-15 Coulomb’s law with Cobra3


4.2.06-00 Dielectric constant of different materials

4.3 Magnetic Field


4.3.02-01/15 Magnetic field of single coils / Biot-Savart’s law


Electricity

4.3.04-00 Magnetic moment in the magnetic field


4.3.06-00 Magnetic field inside a conductor

4.3.07-11 Ferromagnetic hysteresis with PC interface system

4.3.08-00 Magnetostriction with the Michelson interferometer

4.4 Electrodynamics

4.4.01-00 Transformer

4.4.02-01/15 Magnetic induction


4.4.04-01/11 Coil in the AC circuit


4.4.06-01/11 RLC Circuit


4.4.08-00 RC Filters


4.4.10-00 RLC measuring bridge


4.4.12-11 Induction impulse

4.5 Electromagnetic Oscilations and Waves

4.5.02-00 Coupled oscillating circuits

4.5.04-00 Interference of microwaves


4.5.06-00 Diffraction and polarization of microwaves


4.5.09-00 Frustrated total reflection / Microwaves

4.6 Handbooks

Demonstration Experiments Physics – Electricity/Electronics on the Magnetic Board 1 + 2

4LEP_4 09.08.2007 11:55 Uhr Seite 152


Measurement of small resistance 4.1.01-01

Stationary currents Electricity

Principle:The resistances of various DC con-ductors are determined by recordingthe current/voltage characteristic.The resistivity of metal rods and thecontact resistance of connectingcords are calculated.

Tasks:1. To plot the current/voltage char-

acteristics of metal rods (copperand aluminium) and to calculatetheir resistivity.

2. To determine the resistance ofvarious connecting cords by plot-ting their current/voltage charac-teristics and calculating the con-tact resistances.

Current/voltage characteristics of a copper rod and an aluminium rod.


� Ohm’s law� Resistivity� Contact resistance� Conductivity� Four-wire method of

measurement

Heat conductivity rod, Cu 04518.11 1

Heat conductivity rod, Al 04518.12 1













What you need:

Complete Equipment Set, Manual on CD-ROM includedMeasurement of small resistance P2410101

LEP_4 09.08.2007 11:55 Uhr Seite 153



Principle:The electrical resistance of pure met-als increases with increasing tem-perature. The correlation betweenvoltage and current is to be mea-sured using temperature-in- and de-pendent resistors. Determine thework and power of an incandescentbulb.

Current, Power and Work of an incandescent bulb.

Tasks:1. To plot the current/voltage char-

acteristics of Ohm’s resistors andof pure metals and to calculatetheir resistivity.

2. To determine the resistance ofvarious connecting cords by plot-ting their current/characteristicsand calculating the contact resis-tances.

3. To determine the work and powerof an incandescent bulb as a func-tion of the applied voltage.








Lamp socket E 10, G1 17049.00 1

Filament lamps, 12 V/0.1 A 07505.03 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedOhm‘s Law with FG-Module P2410115

Electricity Stationary currents


� Ohm’s law� Resistivity� Contact resistance� Conductivity� Power and Work

You can find more

experiments in Handbook

“Physics Experiments

with Cobra3”

Order No. 01310.02

LEP_4 09.08.2007 11:55 Uhr Seite 154



Wheatstone Bridge 4.1.02-00

Principle:The Wheatstone bridge circuit isused to determine unknown resis-tances. The total resistance of resis-tors connected in parallel and inseries is measured.

Tasks:1. Determination of unknown resist-

ances.

Determination of the total resist-ance

2. of resistors in series,

Resistance of a conductor wire as a function of its radius r.

3. of resistors in parallel.

4. Determination of the resistance ofa wire as a function of its cross-section.

Resistance board, metal 06108.00 1

Simple slide wire measuring bridge 07182.00 1






Carbon resistor G1, 680 Ω, 1 W 39104.17 1

Carbon resistor 1 kΩ, 1W, G1 39104.19 1

Carbon resistor 4.7 kΩ, 1W, G1 39104.27 1



Carbon resistor G1, 82 kΩ, 1 W 39104.40 1


Power supply 5 V-/1 A, +/- 15 V 13502.93 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedWheatstone Bridge P2410200


� Kirchhoff’s laws� Conductor� Circuit� Voltage� Resistance� Parallel connection� Series connection

LEP_4 09.08.2007 11:55 Uhr Seite 155


Principle:Both the terminal voltage of a volt-age source and the current dependon the load, i. e. on the external re-sistance. The terminal voltage ismeasured as a function of the cur-rent and from it the internal resist-ance and no-load voltage of thevoltage source are determined andthe power graph plotted.

Tasks:1. To measure the terminal voltage

Ut of a number of voltage sourceas a function of the current, vary-ing the external resistance Re, andto calculate the no-load voltageU0 and the internal resistance Ri.

1.1 Slimline battery1.2 Power supply1.2.1 Alternating voltage output1.2.2 Direct voltage output

Power diagram of a voltage source.

2. To measure directly the no-loadvoltage of the slimline battery(with no external resistance) andits internal resistance (by powermatching, Ri = Re).

3. To determine the power diagramfrom the relationship betweenterminal voltage and current, asillustrated by the slimline battery.


� Voltage source� Electromotive force (e.m.f.)� Terminal voltage� No-load operation� Short circuit� Ohm’s law� Kirchhoff’s laws� Power matching

Battery box 06030.21 1


Flat cell battery, 4.5 V 07496.01 1


Rheostats, 10 Ω, 5.7 A 06110.02 1

Rheostats, 100 Ω, 1.8 A 06114.02 1


Double socket, pair red and black 07264.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedInternal resistance and matchingin voltage source P2410300



LEP_4 09.08.2007 11:55 Uhr Seite 156



Temperature dependence of different resistors and diodes 4.1.04-01/15

Principle:The temperature dependence of anelectrical parameter (e.g. resistance,conducting-state voltage, blockingvoltage) of different components isdetermined. To do this, the immer-sion probe set is immersed in a waterbath and the resistance is measuredat regular temperature intervals.

Diagram of resistances.

Tasks:1. Measurement of the temperature

dependence of the resistance ofdifferent electrical components.

2. Measurement of the temperaturedependence of the conductingstate voltage of semiconductingdiodes.

3. Measurement of the temperaturedependence of the voltage in theZener and the avalanche effects.


Immersion probes for determining ct 07163.00 1 1

Immersion thermostat TC10 08492.93 1 1

Accessory set for TC10 08492.01 1 1

Bath for thermostat, Makrolon 08487.02 1 1



Carbon resistor 4.7 kΩ, 1W, G1 39104.27 1 1










What you need:

Complete Equipment Set, Manual on CD-ROM includedTemperature dependence of differentresistors and diodes P24104 01/15


� Carbon film resistor� Metallic film resistor� PTC� NTC� Z diode� Avalanche effect� Zener effect� Charge carrier generation� Free path� Mathie’s rule

Set-up of experiment P2410401 with multimeter

LEP_4 09.08.2007 11:55 Uhr Seite 157

4.1.06-01/15 Current balance / Force acting on a current-carrying conductor

Principle:The force acting on a current-carry-ing conductor loop in a uniformmagnetic field (Lorentz force) ismeasured with a balance.

Conductor loops of various sizes aresuspended in turn from the balance,and the Lorentz force is determinedas a function of the current andmagnetic induction. The uniformmagnetic field is generated by anelectromagnet. The magnetic induct-ion can be varied with the coil cur-rent.

Tasks:1. The direction of the force is to be

determined as a function of thecurrent and the direction of themagnetic field.

2. The force F is to be measured, asa function of the current IL in theconductor loop, with a constantmagnetic induction B and forconductor loops of various sizes. The magnetic induction is to becalculated.

3. The force F is to be measured, asa function of the coil current IM,for a conductor loop. In the rangebeing considered, the magneticinduction B is, with sufficient ac-curay, proportional to the coil cur-rent IM.

Lorentz force F as a function of the current IL in the conductor loop.


� Uniform magnetic field� Magnetic induction (formerly

magnetic-flux densitiy)� Lorentz force� Moving charges� Current

Experiment P2410615 with Cobra3Experiment P2410601 with amperemeterAmmeter 1/5 A DC 07038.00 2Tripod base -PASS- 02002.55 2Support rod -PASS-, square, l = 1000 mm 02028.55 1Right angle clamp -PASS- 02040.55 1Balance LGN 310, on rod 11081.01 1Pole pieces, rectangular, 1 pair 11081.02 1 1Wire Loop, l = 12,5 mm, n = 1 11081.05 1 1Wire Loop, l = 25 mm, n = 1 11081.06 1 1Wire loop, l = 50 mm, n = 2 11081.07 1 1Wire Loop, l = 50 mm, n = 1 11081.08 1 1Iron core, U-shaped, laminated 06501.00 1 1Base for iron cores 06508.00 2 2Coil, 900 turns 06512.01 2 2Metal strip with plugs 06410.00 2 2Distributor 06024.00 1 1Bridge rectifier, 30 VAC/1 ADC 06031.10 1 1On/Off switch 06034.01 1 1Power supply, universal 13500.93 1 1Connecting cable, 4 mm plug, 32 A, red, l = 10 cm 07359.01 1 2Connecting cable, 4 mm plug, 32 A, red, l = 25 cm 07360.01 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 25 cm 07360.04 2 3Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 2Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 1 1Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 1 1Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 1 1Support base, variable 02001.00 1Bosshead 02043.00 2Support rod, stainless steel 18/8, l = 1000 mm 02034.00 1Cobra3 BASIC-UNIT, USB 12150.50 1Newton measuring module 12110.00 1Newton Sensor 12110.01 1Cobra3 current probe 6 A 12126.00 2Software Cobra3 PowerGraph 14525.61 1Power supply 12V/2A 12151.99 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedCurrent balance / Force acting on a current-carrying conductor P24106 01/15

158 PHYWE Systeme GmbH & Co. KG · D-37070 GöttingenLaboratory Experiments, Physics



LEP_4 09.08.2007 11:55 Uhr Seite 158

159PHYWE Systeme GmbH & Co. KG · D-37070 Göttingen Laboratory Experiments, Physics


Semiconductor thermogenerator 4.1.07-00

Principle:In a semi-conductor thermogenera-tor, the no-load voltage and theshort-circuit current are measured asa function of the temperature differ-ence. The internal resistance, theSeebeck coefficient and the efficien-cy are determined.

Tasks:1. To measure no-load voltage Uo

and short-circuit current Is at dif-ferent temperature differencesand to determine the Seebeck co-efficient.

2. To measure current and voltage ata constant temperature differencebut with different load resistors,

Electrical power generated as a function of the temperature difference.

and to determine the internal re-sistance Ri from the measuredvalues.

3. To determine the efficiency of en-ergy conversion, from the quantityof heat consumed and the electri-cal energy produced per unit time.

Thermogenerator 04366.00 1

Flow-through heat exchanger 04366.01 2



Rheostats, 33 Ω, 3.1 A 06112.02 1

Voltmeter 0.3...300 V-, 10...300 V~ 07035.00 1

Ammeter 1/5 A DC 07038.00 1







Resistor 2 Ω 2%, 2W, G1 06055.20 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedSemiconductor thermogenerator P2410700


� Seebeck effect (thermoelectric effect)

� Thermoelectric e.m.f.� Efficiency� Peltier coefficient� Thomson coefficient� Seebeck coefficient� Direct energy conversion� Thomson equations

LEP_4 09.08.2007 11:55 Uhr Seite 159


Principle:The cooling capacity heating capac-ity and efficiency rating of a Peltierheat pump are determined under dif-ferent operating conditions.

Tasks:1. To determine the cooling capacity

Pc the pump as a function of thecurrent and to calculate the effi-ciency rating hc at maximum out-put.

2. To determine the heating capacityPw of the pump and its efficiencyrating hw at constant current andconstant temperature on the coldside.

Pump cooling capacity as a function of the operating current.

3. To determine Pw , �w and Pc , �c

from the relationship betweentemperature and time on the hotand cold sides.

4. To investigate the temperaturebehaviour when the pump is usedfor cooling, with the hot side air-cooled.


� Peltier effect� Heat pipe� Termoelectric e.m. f.� Peltier coefficient� Cooling capacity� Heating capacity� Efficiency rating� Thomson coefficient� Seebeck coefficient� Thomson equations� Heat conduction� Convection� Forced cooling� Joule effect

Thermogenerator 04366.00 1

Flow-through heat exchanger 04366.01 1

Air cooler 04366.02 1

Heating coil with sockets 04450.00 1


Rheostats, 33 Ω, 3.1 A 06112.02 1

Connecting plug, pack of 2 07278.05 1


















What you need:

Complete Equipment Set, Manual on CD-ROM includedPeltier heat pump P2410800



LEP_4 09.08.2007 11:55 Uhr Seite 160



Characteristic curves of a solar cell 4.1.09-01

Principle:The current-voltage characteristicsof a solar cell are measured at differ-ent light intensities, the distance be-tween the light source and the solarcell being varied.

The depencence of no-load voltageand short-circuit current on temper-ature is determined.

Tasks:1. To determine the light intensity

with the thermopile at variousdistances from the light source.

2. To measure the short-circuit cur-rent and no-load voltage at vari-ous distances from the lightsource.

3. To estimate the dependence ofno-load voltage, and short-circuitcurrent on temperature.

4. To plot the current-voltage char-acteristic at different light inten-sities.

Current-voltage characteristic at different light intensities J.

5. To plot the current-votlage char-acteristic under different operat-ing conditions: cooling the equip-ment with a blower, no cooling,shining the light through a glassplate.

6. To determine the characteristiccurve when illuminating by sun-light.

Solar battery, 4 cells, 2.5 x 5 cm 06752.04 1

Thermopile, Moll type 08479.00 1


Rheostats, 330 Ω, 1.0 A 06116.02 1

Ceramic lamp socket E27 with reflector, switch, safety plug 06751.01 1

Filament lamp with reflector, 230 V/120 W 06759.93 1


Meter Scale, l = 1000 x 27 mm 03001.00 1







G-clamp 02014.00 2

Glass pane, 150 x 100 x 4 mm, 2 off 35010.10 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristic curves of a solar cell P2410901


� Semiconductor� p-n junction� Energy-band diagram� Fermi characteristic energy

level� Diffusion potential� Internal resistance� Efficiency� Photo-conductive effect� Acceptors� Donors� Valence band� Conduction band

LEP_4 09.08.2007 11:55 Uhr Seite 161




Principle:Determine the current strengthflowing through a semi-conductingdiode.

Determine the collector current withthe collector voltage for various val-ues of the base current intensity.

Collector current/voltage characteristic of BC337 transistor.

Tasks:1. To investigate the dependence of

the current strength flowingthrough a semi-conducting diode.

2. To determine the variations of thecollector current with the collec-tor voltage for varios values of thebase current intensity.


� Semiconductor� P-n junction� Energy-band diagram� Acceptors� Donors� Valence band� Conduction band� Transistor� Operating point






Potentiometer 1 kΩ, 0.4W, G2 39103.04 1

Plug-in board 4 mm plugs 06033.00 1

Transistors BC-337/40, in G3 casing 39127.20 1


Silicon diode 1 N 4007, G1 39106.02 1

Silicon diode 1 N 4148, G1 39106.03 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristic curves of semiconductorswith FG-Module P2410915

LEP_4 09.08.2007 11:55 Uhr Seite 162


Characteristic and efficiency of PEM fuel cell and PEM electrolyser 4.1.11-00


Principle:In a PEM electrolyser, the electrolyteconsists of a proton-conductingmembrane and water (PEM = Pro-ton-Exchange-Membrane). When anelectric voltage is applied, hydrogenand oxygen are formed. The PEM fuelcell generates electrical energy fromhydrogen and oxygen.

The electrical properties of the elec-trolyser and the fuel cell are investi-gated by recording a current-voltagecharacteristic line. To determine theefficiency, the gases are stored insmall gasometers in order to be ableto measure the quantities of thegases generated or consumed.

Volume of the hydrogen generated by the PEM electrolyser as a function oftime at different current I.

Tasks:1. Recording the characteristic line

of the PEM electrolyser.

2. Recording the characteristic lineof the PEM fuel cell.

3. Determination of the efficiency ofthe PEM electrolysis unit.

4. Determination of the efficiency ofthe PEM fuel cell.


� Electrolysis� Electrode polarisation� Decomposition voltage� Galvanic elements� Faraday’s law

PEM fuel cell 06747.00 1

PEM electrolyser 06748.00 1


Resistor 10 Ω 2%, 2W, G1 06056.10 2

Resistor 5 Ω 2%, 2W, G1 06055.50 1

Resistor 2 Ω 2%, 2W, G1 06055.20 1

Resistor 1 Ω 2%, 2W, G1 06055.10 2

Short-circuit plug, black 06027.05 2

Gas bar 40466.00 1

Graduated cylinder, 100 ml, plastic 36629.01 1




Hose connector, reducing, d = 3-5/6-10 mm 47517.01 2


Beaker, 250 ml, low form, plastic 36013.01 1











What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristic and efficiencyof PEM fuel cell and PEM electrolyser P2411100

LEP_4 09.08.2007 11:55 Uhr Seite 163



Principle:The correlation between theamounts of substances transformedin the electrode reaction and the ap-plied charge (amount of electricity)is described by Faraday´s law. Fara-day´s constant, which appears as aproportionality factor, can be deter-mined experimentally from this de-pendence.

Correlations between the transferred charge and the evolved volumes of hy-drogen and oxygen in the electrolysis of diluted sulphuric acid (T = 296.05 Kand p = 100.4 kPa)

Tasks:Determine Faraday´s constant fromthe dependence of the volumes ofhydrogen and oxygen evolved on theapplied charge in the hydrolysis ofdiluted sulphuric acid.

Power supply, universal 13500.93 1Digital multimeter 2010 07128.00 1Electrolysis apparatus - Hofmann 44518.00 1Platinum electrode in protective tube, d = 8 mm 45206.00 2On/Off switch 06034.01 1Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 1Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 1Connecting cable, 4 mm plug, 32 A, red, l = 25 cm 07360.01 2Retort stand, h = 750 mm 37694.00 1Right angle clamp 37697.00 4Universal clamp 37718.00 3Stopwatch, digital, 1/100 s 03071.01 1Barometer/Manometer, hand-held 07136.00 1Digital thermometer, NiCr-Ni 07050.00 1Beaker, DURAN®, short form, 600 ml 36015.00 1Precision Balance, Sartorius LE 623P 45023.93 1Pasteur pipettes, l = 145 ml 36590.00 1Rubber caps, 10 pcs 39275.03 1Funnel, glass, d = 80 mm 34459.00 1Wash bottle, plastic, 500 ml 33931.00 1Sulphuric acid, 95-98%, 500 ml 30219.50 1Water, distilled 5 l 31246.81 1Weather monitor, 6 lines LCD 87997.10 1Precision Balance, Sartorius LE 623P 48852.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFaraday’s law P2411200



� Electrolysis� Coulometry� Charge� Amount of substance� Faraday´s law� Faraday´s contant� Avogadro´s number� General equation of state for

ideal gases

LEP_4 09.08.2007 11:55 Uhr Seite 164


Second order conductors. Electrolysis with FG-Module 4.1.13-15


Principle:In this experiment a copper(II) sul-phate solution is to be electrolysedusing two different materials -graphite electrodes and copperwires. During the electrolyses thecurrent/voltage curves are recorded.

Current/voltage characteristics of an aqueous copper sulphate solution con-ducted with graphite electrodes and copper wires.

Tasks:Measure the correlation betweenvoltage and current on second orderconductors (copper (II) sulphate so-lution using two different materials -graphite electrodes and copperwires.


� Electrolysis� Electrode polarisation� Conductivity� Ohm’s law





Retort stand, 210 mm x 130 mm, h = 500 mm 37692.00 1


Support for two electrodes 45284.01 1

Graphite electrodes, d = 5 mm, l = 150 mm, 6 pcs. 44510.00 1

Copper wire, d = 0.5 mm 06106.03 1


Graduated cylinder, BORO 3.3, 100 ml 36629.00 1

Precision Balance, Sartorius TE 412 48835.93 1

Spoon with spatula end, l = 150 mm, steel, wide 33398.00 1



Copper-II sulphate, cryst., 250 g 30126.25 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedSecond order conductors.Electrolysis with FG-Module P2411315

LEP_4 09.08.2007 11:55 Uhr Seite 165


Electricity Electric field


Principle:A uniform electric field E

�is pro-

duced between the charged plates ofa plate capacitor. The strength of thefield is determined with the electricfield strength meter, as a function ofthe plate spacing d and the voltageU. The potential � within the field ismeasured with a potential measur-ing probe.

Tasks:1. The relationship between voltage

and electric field strength is inves-tigated, with constant plate spac-ing.

2. The relationship between electricfield strength and plate spacing isinvestigated, with constant volt-age.

Electric field strength as a function of the plate voltage.

3. In the plate capacitor, the poten-tial is measured with a probe, as afunction of position.


� Capacitor� Electric field� Potential� Voltage� Equipotential lines

Capacitor plate 283 mm x 283 mm 06233.02 2

Capacitor plate with hole, d = 55 mm 11500.01 1

Spacer plates, 1 set 06228.01 1

Electric field meter 11500.10 1

Potential probe 11501.00 1

Power supply, regulated, 0...600 V- 13672.93 1

Blow lamp, butan cartridge, X2000 46930.00 1




Connecting cable, 4 mm plug, 32 A, green-yellow, l = 10 cm 07359.15 1













High value resistors, 10 MΩ 07160.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedElectrical fields and potentialsin the plate capacitor P2420100

LEP_4 09.08.2007 11:55 Uhr Seite 166


Electric field Electricity

Charging curve of a capacitor 4.2.02-01

Principle:A capacitor is charged by way of aresistor. The current is measured as afunction of time and the effects ofcapacitance, resistance and the volt-age applied are determined.

Tasks:To measure the charging currentover time:

1. using different capacitance valuesC, with constant voltage U andconstant resistance R

2 using different resistance values(C and U constant)

Course of current with time at different capacitance values; voltage andresistance are constant (U = 9 V, R = 2.2 M�).

3. using different voltages (R and Cconstant).

To determine the equation repre-senting the current when a capacitoris being charged, from the valuesmeasured.


Two way switch, single pole 06030.00 1

Capacitor 2 x 30 µF 06219.32 1


Carbon resistor 1 MΩ, 1W, G1 39104.52 4

Connecting plug white 19 mm pitch 39170.00 2

Capacitor 1 microF/ 250 V, G2 39113.01 1

Capacitor 4,7 microF/ 250 V, G2 39113.03 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedCharging curve of a capacitor P2420201


� Charging� Discharging� Time constant� Exponential function� Half life

LEP_4 09.08.2007 11:55 Uhr Seite 167




Principle:To measure the course of currentstrength and voltage ina capaci-tance/inductivity in the instant ofswitching on. The capacitance/in-ductivity is determined from themeasurement curve.

The course of the voltage and the current intensity during a switching onprocess in a capacitance.

Tasks:1. To measure the course of current

strength and voltage in a capaci-tance in the instant of switchingon. The capacitance is determinedfrom the measurement curve.

2. To measure the course of currentstrength and voltage in inductivityin the instant of switching on. Theinductivity is determined from themeasurement curve.






On/Off switch 06034.01 1



Electrolyte capacitors non-polarised, G1, 47 µF 39105.45 1

Coil, 900 turns 06512.01 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedSwitch-on behaviour of a capacitor and an inductivity with FG-Module P2420215


� Charging� Discharging� Time constant� Exponential function� Half life

The course of the voltage and the current intensity during a switching onprocess in a coil.

LEP_4 09.08.2007 11:55 Uhr Seite 168


Capacitance of metal spheres and of a spherical capacitor 4.2.03-00


Principle:Metal spheres with different radiiand a spherical capacitor arecharged by means of a variable volt-age. The induced charges are deter-mined with a measuring amplifier.The corresponding capacitances arededuced from voltage and chargevalues.

Tasks:1. Determination of the capacitance

of three metal spheres with differ-ent diameters.

2. Determination of the capacitanceof a spherical capacitor.

U1 (measured voltage) as a function of U2 (charging voltage) measured onconducting spheres with three different diameters.

3. Determination of the diameters ofeach test body and calculation oftheir capacitance values.


� Voltage� Potential� Charge� Electric field� Electrostatic induction� Electrostatic induction

constant� Capacitance� Capacitor� Dielectrics

Conducting ball, d = 20 mm 06236.00 2Conducting ball, d = 40 mm 06237.00 1Conducting ball, d = 120 mm 06238.00 1Hemispheres, Cavendish type 06273.00 1Hollow plastic ball with eyelet 06245.00 1Capillary tube, AR-glass, straight, l = 250 mm 36709.00 1Copper wire, d = 0.5 mm 06106.03 1Insulating stem 06021.00 2High value resistors, 10 MΩ 07160.00 1High voltage supply 0...10 kV 13670.93 1Capacitor 10 nF/ 250 V, G1 39105.14 1Universal measuring amplifier 13626.93 1Multi range meter, analogue 07028.01 1Digital multimeter 2010 07128.00 1Connecting cable, 30 kV, l = 1000 mm 07367.00 1Screened cable, BNC, l = 750 mm 07542.11 1Adapter, BNC socket - 4 mm plug 07542.20 1T type connector, BNC, socket, socket, plug 07542.21 1Adapter, BNC plug/4 mm socket 07542.26 1Vernier caliper, plastic 03011.00 1Barrel base -PASS- 02006.55 2Support base -PASS- 02005.55 1Right angle clamp -PASS- 02040.55 4Support rod -PASS-, square, l = 630 mm 02027.55 1Support rod -PASS-, square, l = 400 mm 02026.55 1Universal clamp with joint 37716.00 1Crocodile clips, black, strong version, pack of 10 29426.03 1Connecting cable, 4 mm plug, 32 A, green-yellow, l = 10 cm 07359.15 1Connecting cable, 4 mm plug, 32 A, green-yellow, l = 75 cm 07362.15 2Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 2Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedCapacitance of metal spheresand of spherical capacitor P2420300

LEP_4 09.08.2007 11:55 Uhr Seite 169



Principle:A small electrically charged ball ispositioned at a certain distance infront of a metal plate lying at earthpotential. The surface charge on theplate due to electrostatic inductiontogether with the charged ball formsan electric field analogous to thatwhich exists between two oppositelycharged point garges.

The electrostatic force acting on theball can be measured with a sensitivetorsion dynamometer.

Tasks:1. Establishment of the relation

between the active force and thecharge on the ball.

2. Establishment of the relationbetween force and distance, ballto metal plate.

Relationship between electrostatic force F and the square of the charge Qfor various distances (a) between ball and plate.

3. Determination of the electric con-stant.

Capacitor plate 283 mm x 283 mm 06233.02 1

Insulating stem 06021.00 2

Conducting ball, d = 40 mm 06237.00 2

Conducting spheres with suspension 02416.01 1

Torsion dynamometer, 0.01 N 02416.00 1



Direct current measuring amplifier 13620.93 1

Power supply, high voltage, 0-25 kV 13671.93 1


Connecting cable, 30 kV, l = 1000 mm 07367.00 1










Holder for U-magnet 06509.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedCoulomb’s law / Image charge P2420401



� Electric field� Electric field strenght� Electric flux� Electrostatic induction� Electric constant� Surface charge density� Dielectric displacement� Electrostatic potential

LEP_4 09.08.2007 11:55 Uhr Seite 170


Coulomb’s law with Cobra3 4.2.04-15

Principle:A small electrically charged ball ispositioned at a certain distance infront of a second charged ball. Theforce between these balls is mea-sured as a function of their chargeand distance (Coulomb’s law). Forthe measurements a sensitive forcesensor and an electrometer amplifierare used.

The force as a function of 1/r2, where r is the distance between the balls.

Tasks:1. Measure the force between two

small electrically charged balls asa function of their charge if bothballs are positively charged (+ +),both negatively (- -) or one posi-tive one negative (+ -).

2. Measure the force between thecharged balls as a function of thedistance.

3. Compare the measured resultswith theoretical values.


� Electric field strength � Electrostatic induction � Surface charge density� Dielectric displacement� Electrostatic potential� Law of distance





Insulating bar for Force Sensor 12110.02 1

Plug with socket and crosshole, 2 pcs. 07206.01 1












Electrometer Amplifier 13621.00 1

Data cable for Cobra probes 12150.07 1


Capacitor 10 nF/ 250 V, G1 39105.14 1

Power supply 12V AC/500 mA 11074.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedCoulomb’s law with Cobra3 P2420415


LEP_4 09.08.2007 11:55 Uhr Seite 171




Principle:Conducting spheres with differentdiameters are charged electrically.The static potentials and the accom-panying electric field intensities aredetermined by means of an electricfield meter with a potential measur-ing probe, as a function of positionand voltage.

Field strenght as a function ofvoltage.

Graphs 1-3: sphere with 2R = 12 cm;r1 = 25 cm, r2 = 50 cm, r3 = 75 cm;graph 4: sphere with 2R = 4 cm; r1 = 25 cm.

Tasks:1. For a conducting sphere of diame-

ter 2R = 12 cm, electrostatic po-tential is determined as a functionof voltage at a constant distancefrom the surface of the sphere.

2. For the conducting spheres of dia-meters 2R = 12 cm and 2R = 4 cm,electrostatic potential at constantvoltage is determined as a func-tion of the distance from the sur-face of the sphere.

3. For both conducting spheres, elec-tric field strenght is determined asa function of charging voltage atthree different distances from thesurface of the sphere.

4. For the conducting sphere of dia-meter 2R = 12 cm, electric fieldstrenght is determined as a func-tion of the distance from the sur-face of the sphere at constantcharging voltage.


� Electric field� Field intensity� Electric flow� Electric charge� Gaussian rule� Surface charge density� Induction� Induction constant� Capacitance� Gradient� Image charge� Electrostatic potential� Potential difference

Electric field meter 11500.10 1

Potential probe 11501.00 1

Capacitor plate with hole, d = 55 mm 11500.01 1






Insulating stem 06021.00 2






Meter Scale, l = 1000 x 27 mm 03001.00 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedCoulomb potential and Coulomb fieldof metal spheres P2420500

LEP_4 09.08.2007 11:55 Uhr Seite 172



XX

X

X

X

XX

XX

X

X

X

X

X

X

X

1000

800

600

400

200

0

1,0 2,0 3,0 4,0

plastic

air

Principle:The electric constant �0 is deter-mined by measuring the charge of aplate capacitor to which a voltage isapplied. The dielectric constant � isdetermined in the same way, withplastic or glass filling the spacebetween the plates.

Tasks:1. The relation between charge Q

and voltage U is to be measuredusing a plate capacitor.

2. The electric constant �0 is to bedetermined from the relationmeasured under point 1.

3. The charge of a plate capacitor isto be measured as a function ofthe inverse of the distancebetween the plates, under con-stant voltage.

Electrostatic charge Q of a plate capacitor as a function of the applied volt-age Uc, with and without dielectric (plastic) between the plates (d = 0.98 cm)

4. The relation between charge Qand voltage U is to be measuredby means of a plate capacitor,between the plates of which dif-ferent solid dielectric media areintroduced. The correspondingdielectric constants are deter-mined by comparison with meas-urements performed with airbetween the capacitor plates.

Plate capacitor, d = 260 mm 06220.00 1

Plastic plate 283 x 283 mm 06233.01 1

Glass plate for current conductors 06406.00 1




Capacitor 220 nF/250 V, G2 39105.19 1

Voltmeter 0.3...300 V-, 10...300 V~ 07035.00 1







T type connector, BNC, socket, socket, plug 07542.21 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedDielectric constant of different materials P2420600


� Maxwell’s equations� Electric constant� Capacitance of a plate

capacitor� Real charges� Free charges� Dielectric displacement� Dielectric polarisation� Dielectric constant

QnAs

Dielectric constant of different materials 4.2.06-00

Uc

kV

LEP_4 09.08.2007 11:55 Uhr Seite 173


Electricity Magnetic field


Principle:A constant magnetic field, its magni-tude and direction known, is super-imposed on the unknown earth-magnetic field. The earth-magneticfield can then be calculated from themagnitude and direction of the re-sulting flux density.

Linear function to determine the horizontal component hBE of the magneticflux density of the earth-magnetic field.

Tasks:1. The magnetic flux of a pair of

Helmholtz coils is to be deter-mined and plotted graphically asa function of the coil current. TheHelmholtz system calibration fac-tor is calculated from the slope ofthe line.

2. The horizontal component of theearth-magnetic field is deter-mined through superimposition ofthe Helmholtz field.

3. The angle of inclination must bedetermined in order to calculatethe vertical component of theearth-magnetic field.


� Magnetic inclination and declination

� Isoclinic lines� Isogenic lines� Inclinometer� Magnetic flow density� Helmholtz coils

Helmholtz coils, one pair 06960.00 1


Rheostats, 100 Ω, 1.8 A 06114.02 1

Teslameter, digital 13610.93 1

Hall probe, axial 13610.01 1


Magnetometer 06355.00 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedEarth’s magnetic field P2430100

LEP_4 09.08.2007 11:55 Uhr Seite 174


Magnetic field Electricity

Magnetic field of single coils / Biot-Savart’s law 4.3.02-01/15

Principle:The magnetic field along the axis ofwire loops and coils of different di-mensions is measured with a tesla-meter (Hall probe). The relationshipbetween the maximum field strengthand the dimensions is investigatedand a comparison is made betweenthe measured and the theoretical ef-fects of position.

Tasks:1. To measure the magnetic flux

density in the middle of variouswire loops with the Hall probe andto investigate its dependence onthe radius and number of turns.

Curve of magnetic flux density (measured values) for coils with a constantdensity of turns n/l, coils radius R = 20 mm, lengths l1 = 53 mm, l2 = 105 mmand l3 = 160 mm.

2. To determine the magnetic fieldconstant �0.

3. To measure the magnetic fluxdensity along the axis of long coilsand compare it with theoreticalvalues.

Experiment P2430215 with Cobra3Experiment P2430201 with teslameter

Teslameter, digital 13610.93 1Digital multimeter 2010 07128.00 1Induction coil, 300 turns, d = 40 mm 11006.01 1 1Induction coil, 300 turns, d = 32 mm 11006.02 1 1Induction coil, 300 turns, d = 25 mm 11006.03 1 1Induction coil, 200 turns, d = 40 mm 11006.04 1 1Induction coil, 100 turns, d = 40 mm 11006.05 1 1Induction coil, 150 turns, d = 25 mm 11006.06 1 1Induction coil, 75 turns, d = 25 mm 11006.07 1 1Conductors, circular, set 06404.00 1 1Hall probe, axial 13610.01 1 1Power supply, universal 13500.93 1 1Distributor 06024.00 1 1Meter Scale, l = 1000 x 27 mm 03001.00 1 1Barrel base -PASS- 02006.55 2 2Support rod -PASS-, square, l = 250 mm 02025.55 1 1Right angle clamp -PASS- 02040.55 1 2G-clamp 02014.00 2 2Lab jack, 200 x 230 mm 02074.01 1 1Reducing plug 4 mm/2 mm socket, 1 pair 11620.27 1 1Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 1 1Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 2 2Bench clamp -PASS- 02010.00 1Plate holder, opening width 0...10 mm 02062.00 1Silk thread on spool, l = 200 mm 02412.00 1Weight holder, 1g, silver bronzing 02407.00 1Cobra3 BASIC-UNIT, USB 12150.50 1Software Cobra3 Force/Tesla 14515.61 1Cobra3 measuring module Tesla 12109.00 1Cobra3 current probe 6 A 12126.00 1Movement sensor with cable 12004.10 1Adapter BNC socket/4 mm plug pair 07542.27 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetic field of a single coils /Biot-Savart’s law P24302 01/15


� Wire loop� Biot-Savart’s law� Hall effect� Magnetic field� Induction� Magnetic flux density

Adapter, BNC socket - 4 mm plug 07542.20 1Power supply 12V/2A 12151.99 1PC, Windows® 95 or higher


LEP_4 09.08.2007 11:55 Uhr Seite 175




Principle:The spatial distribution of the fieldstrength between a pair of coils inthe Helmholtz arrangement is mea-sured. The spacing at which a uni-form magnetic field is produced isinvestigated and the superposition ofthe two individual fields to form thecombined field of the pair of coils isdemonstrated.

Tasks:1. To measure the magnetic flux

density along the z-axis of the flatcoils when the distance betweenthem a = R (R = radius of thecoils) and when it is larger andsmaller than this.

2. To measure the spatial distributionof the magnetic flux density whenthe distance between coils a = R,using the rotational symmetry ofthe set-up:

a) measurement of the axial com-ponent Bz

B (r = 0; r is the distance perpendicular to the axis of the coils) as a functionof z (z is the distance from the center of the coils in the direction of the axisof the coils) with the parameter �.

b) measurement of radial compo-nent Br.

3. To measure the radial componentsB�r and B�r of the two individualcoils in the plane midway betweenthem and to demonstrate theoverlapping of the two fields at Br = 0.


� Maxwell’s equations� Wire loop� Flat coils� Biot-Savart’s law� Hall effect




Helmholtz coils, one pair 06960.00 1 1

Power supply, universal 13500.93 1 1

Hall probe, axial 13610.01 1 1

Meter Scale, l = 1000 x 27 mm 03001.00 2 2

Barrel base -PASS- 02006.55 1 1



G-clamp 02014.00 3 3









Cobra3 measuring module Tesla 12109.00 1

Cobra3 current probe 6 A 12126.00 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetic field of paired coilsin Helmholtz arrangement P24303 01/15


LEP_4 09.08.2007 11:55 Uhr Seite 176



What you need:

Magnetic moment in the magnetic field 4.3.04-00

Principle:A conductor loop carrying a currentin a uniform magnetic field experi-ences a torque. This is determined asa function of the radius, of the num-ber of turns and the current in theconductor loop and of the strengthof the external field.

Tasks:Determination of the torque due to amagnetic moment in a uniform mag-netic field, as a function

1. of the strength of the magneticfield,

Torque due to a magnetic moment in a uniform magnetic field as a functionof the angle between the magnetic field and magnetic moment.

2. of the angle between the mag-netic field in the magnetic mo-ment,

3. of the strength of the magneticmoment.


Conductors, circular, set 06404.00 1

Torsion dynamometer, 0.01 N 02416.00 1

Coil carrier for torsion dynamometer 02416.02 1



Variable transformer with rectifier 15 V~/12 V- , 5 A 13530.93 1







Complete Equipment Set, Manual on CD-ROM includedMagnetic moment in the magnetic field P2430400

� Torque� Magnetic flux� Uniform magnetic field� Helmholtz coils


LEP_4 09.08.2007 11:55 Uhr Seite 177




Principle:A current which flows through oneor two neighbouring straight con-ductors produces a magnetic fieldaround them. The dependences ofthese magnetic fields on the dis-tance from the conductor and on thecurrent are determined.

Tasks:Determination of the magnetic field

1. of a straight conductor as a func-tion of the current,

2. of a straight conductor as a func-tion of the distance from the con-ductor,

3. of two parallel conductors, inwhich the current is flowing inthe same direction, as a function

Magnetic field component By of two parallel conductors on the x-axis as afunction of the distance from one conductor, if the current in both conduc-tors is in the same direction.

of the distance from one conduc-tor on the line joining the twoconductors,

4. of two parallel conductors, inwhich the current is flowing inopposite directions, as a functionof the distance from one conduc-tor on the line joining the twoconductors.

� Maxwell’s equations� Magnetic flux� Induction� Superimposition of magnetic

fields

Electric conductors, set of 4 06400.00 1

Coil, 6 turns 06510.00 1

Coil, 140 turns, 6 tappings 06526.01 1

Clamping device 06506.00 1

Iron core, rod shaped, laminated 06500.00 1


Variable transformer with rectifier 15 V~/12 V- , 5 A 13530.93 1


Hall probe, axial 13610.01 1

Current transformer/Clamp Ampermeter adaptor 07091.00 1


Meter Scale, l = 1000 x 27 mm 03001.00 1




G-clamp 02014.00 2


Complete Equipment Set, Manual on CD-ROM includedMagnetic field outside a straight conductor P2430500

What you need:


LEP_4 09.08.2007 11:55 Uhr Seite 178



Magnetic field inside a conductor 4.3.06-00

Principle:A current which produces a magnet-ic field is passed through an electro-lyte. This magnetic field inside theconductor is determined as a func-tion of position and current.

Magnetic field inside a conductor as a function of the position x (x = heightof the probe perpendicular to the axis of the cylinder).

Tasks:Determination of the magnetic fieldinside a conductor as a function

1. of the current in the conductor,

2. of the distance from the axis ofthe conductor.

Hollow cylinder, PLEXIGLAS 11003.10 1

Search coil, plane 11004.00 1






Meter Scale, l = 1000 x 27 mm 03001.00 1









Hydrochloric acid 37 %, 1000 ml 30214.70 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetic field inside a conductor P2430600


� Maxwell’s equations� Magnetic flux� Induction� Current density� Field strength

LEP_4 09.08.2007 11:55 Uhr Seite 179



4.3.07-11 Ferromagnetic hysteresis with PC interface system

Principle:A magnetic field is generated in aring-shaped iron core by a continu-ous adjustable direct current appliedto two coils. The field strength Hand the flux density B are measuredand the hysteresis recorded.

The remanence and the coercive fieldstrength of two different iron corescan be compared.

Hysteresis for a massive iron core.

Tasks:Record the hysteresis curve for amassive iron core and for a laminat-ed one.


� Induction� Magnetic flux, coil� Magnetic field strength� Magnetic field of coils� Remanence� Coercive field strength

Coil, 600 turns 06514.01 2

Iron core, U-shaped, solid 06491.00 1

Iron core, rod shaped, solid 06490.00 1



Commutator switch 06034.03 1

Power supply, universal, with analog display 13501.93 1

Rheostats, 10 Ω, 5.7 A 06110.02 1

Hall probe, tangential, with protective cap 13610.02 1



Support rod with hole, stainless steel, l = 150 mm 02030.15 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedFerromagnetic hysteresis with PC interface system P2430711

LEP_4 09.08.2007 11:55 Uhr Seite 180


Magnetostriction with the Michelson interferometer 4.3.08-00


Principle:With the aid of two mirrors in aMichelson arrangement, light isbrought to interference. Due to themagnetostrictive effect, one of themirrors is shifted by variation in themagnetic field applied to a sample,and the change in the interferencepattern is observed.

Measuring results of the magnetostriction of nickel with the relative changein length �l/l plotted against applied field strength H.

Tasks:1. Construction of a Michelson inter-

ferometer using separate opticalcomponents.

2. Testing various ferromagnetic ma-terials (iron and nickel) as well asa non-ferromagnetic material(copper), with regard to theirmagnetostrictive properties.


� Interference� Wavelength� Diffraction index� Speed of light� Phase� Virtual light source� Ferromagnetic material� Weiss molecular magnetic

fields� Spin-orbit coupling


Laser, He-Ne 0.2/1.0 mW, 220 V AC* 08180.93 1




Holder for diaphragm/ beam plitter 08719.00 1

Beam plitter 1/1, non polarizing 08741.00 1

Lens, mounted, f = +20 mm 08018.01 1


Screen, white, 150 x 150 mm 09826.00 1

Faraday modulator for optical base plate 08733.00 1

Rods for magnetotriction, set of 3 08733.01 1





*Alternative:



What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetostriction with the Michelson interferometer P2430800

LEP_4 09.08.2007 11:55 Uhr Seite 181


Electricity Electrodynamics

4.4.01-00 Transformer

Principle:An alternating voltage is applied toone of two coils (primary coil) whichare located on a common iron core.The voltage induced in the secondcoil (secondary coil) and the currentflowing in it are investigated asfunctions of the number of turns inthe coils and of the current flowingin the primary coil.

Tasks:The secondary voltage on the opencircuited transformer is determinedas a function1. of the number of turns in the

primary coil,2. of the number of turns in the

secondary coil,3. of the primary voltage.

The short-circuit current on the sec-ondary side is determined as a func-tion4. of the number of turns in the pri-

mary coil,

Secondary short-circuit current of the transformer as a function1. of the number of turns in the secondary coil,2. of the number of turns in the primary coil.

5. of the number of turns in thesecondary coil,

6. of the primary current.

With the transformer loaded, theprimary current is determined as afunction7. of the secondary current,8. of the number of turns in the

secondary coil,9. of the number of turns in the

primary coil.

Coil, 140 turns, 6 tappings 06526.01 2




Multi-tap transformer with rectifier 14 VAC/12 VDC, 5 A 13533.93 1

Two-way switch, double pole 06032.00 1

Rheostats, 10 Ω, 5.7 A 06110.02 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedTransformer P2440100


� Induction� Magnetic flux� Loaded transformer� Unloaded transformer� Coil

LEP_4 09.08.2007 11:55 Uhr Seite 182


Magnetic Induction 4.4.02-01/15

Electrodynamics Electricity

Principle:A magnetic field of variable frequen-cy and varying strength is producedin a long coil. The voltages inducedacross thin coils which are pushedinto the long coil are determined asa function of frequency, number ofturns, diameter and field strength.

Induced voltage as a function of current for different coils.

Tasks:Determination of the induction volt-age as a function

1. of the strength of the magneticfield,

2. of the frequency of the magneticfield,

3. of the number of turns of the in-duction coil,

4. of the cross-section of the induc-tion coil.


� Maxwell’s equations� Electrical eddy field� Magnetic field of coils� Coil� Magnetic flux� Induced voltage

Experiment P2440215 with FG-ModuleExperiment P2440201 with counter




Field coil 750 mm, 485 turns/m 11001.00 1 1

Induction coil, 300 turns, d = 40 mm 11006.01 1 1
















What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetic Induction P24402 01/15


LEP_4 09.08.2007 11:55 Uhr Seite 183


Principle:A square wave voltage of low fre-quency is applied to oscillatory cir-cuits comprising coils and capacitorsto produce free, damped oscillations.The values of inductance are calcu-lated from the natural frequenciesmeasured, the capacitance beingknown.

Tasks:To connect coils of different dimen-sions (length, radius, number ofturns) with a known capacitance Cto form an oscillatory circuit. Fromthe measurements of the natural fre-quencies, to calculate the induc-

Inductance per turn as a function of the length of the coil at constant radius.

tances of the coils and determine therelationships between:

1. inductance and number of turns

2. inductance and length

3. inductance and radius.


� Lenz’s law� Self-inductance� Solenoids� Transformer� Oscillatory circuit� Resonance� Damped oscillation� Logarithmic decrement� Q factor

Experiment P2440311 with FG-ModuleExperiment P2440301 with oscilloscope

Function generator 13652.93 1Oscilloscope 30 MHz, 2 channels 11459.95 1Adapter, BNC plug/4 mm socket 07542.26 1Induction coil, 300 turns, d = 40 mm 11006.01 1 1Induction coil, 300 turns, d = 32 mm 11006.02 1 1Induction coil, 300 turns, d = 25 mm 11006.03 1 1Induction coil, 200 turns, d = 40 mm 11006.04 1 1Induction coil, 100 turns, d = 40 mm 11006.05 1 1Induction coil, 150 turns, d = 25 mm 11006.06 1 1Induction coil, 75 turns, d = 25 mm 11006.07 1 1Coil, 1200 turns 06515.01 1 1Capacitor 470 nF/250 V, G1 39105.20 1 1Connection box 06030.23 1 1Connecting cable, 4 mm plug, 32 A, red, l = 25 cm 07360.01 1 1Connecting cable, 4 mm plug, 32 A, blue, l = 25 cm 07360.04 1 1Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 2 2Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 2Software Cobra3 Universal recorder 14504.61 1Software Cobra3 PowerGraph 14525.61 1Measuring module Function Generator 12111.00 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedInductance of solenoids with Cobra3 P24403 01/11



Measurement of the oscillation period with the “Survey Function”.


LEP_4 09.08.2007 11:55 Uhr Seite 184



Coil in the AC circuit 4.4.04-01/11

Principle:The coil is connected in a circuit witha voltage source of variable frequen-cy. The impedance and phase dis-placements are determined as func-tions of frequency. Parallel and seriesimpedances are measured.

Tangent of the current-voltage phase displacement as a function of thefrequency used for calculation of the total inductance of coils connected inparallel and in series.

Tasks:1. Determination of the impedance

of a coil as a function of frequen-cy.

2. Determination of the inductanceof the coil.

3. Determination of the phase dis-placement between the terminalvoltage and total current as afunction of the frequency in thecircuit.

4. Determination of the totalimpedance of coils connected inparallel and in series.


� Inductance � Kirchhoff’s laws � Maxwell’s equations � AC impedance� Phase displacement




Difference amplifier 11444.93 1




Coil, 300 turns 06513.01 1 1

Coil, 600 turns 06514.01 1 1











Carbon resistor 47 Ω, 1W, G1 39104.62 1 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedCoil in the AC circuit P24404 01/11


LEP_4 09.08.2007 11:55 Uhr Seite 185




Principle:A capacitor is connected in a circuitwith a variable-frequency voltagesource. The impedance and phasedisplacement are determined as afunction of frequency and of capaci-tance. Parallel and series impedancesare measured.

Impedance of various capacitors as a function of the frequency.

Tasks:1. Determination of the impedance

of a capacitor as a function offrequency.

2. Determination of the phase dis-placement between the terminalvoltage and total current as afunction of the frequency in thecircuit.

3. Determination of the totalimpedance of capacitors connect-ed in parallel and in series.











Capacitor 1 microF/ 250 V, G2 39113.01 1 1

Capacitor 4,7microF/ 250 V, G2 39113.02 1 1











What you need:

Complete Equipment Set, Manual on CD-ROM includedCapacitor in the AC circuit P24405 01/15


� Capacitance� Kirchhoff’s laws� Maxwell’s equations� AC impedance� Phase displacement


LEP_4 09.08.2007 11:55 Uhr Seite 186



RLC Circuit 4.4.06-01/11

Principle:The current and voltage of paralleland series-tuned circuits are investi-gated as a function of frequency. Q-factor and bandwidth are deter-mined.

Tasks:Determination of the frequency per-formance of a

1. Series-tuned circuit for

a) voltage resonance withoutdamping resistor,

b) current resonance withoutdamping resistor,

c) current resonance with damp-ing resistor.

Total voltage as a function of frequency in the parallel tuned circuit. Curvesrecorded for different resistors(top down): R = ∞ Ω, 1000 Ω, 470 Ω.


� Series-tuned circuit� Parallel-tuned circuit� Resistance� Capacitance� Inductance� Capacitor� Coil� Phase displacement� Q factor � Band-width� Loss resistance � Damping





Coil, 300 turns 06513.01 1 1

Connecting plug white 19 mm pitch 39170.00 2 2




Carbon resistor 1kΩ, 1W, G1 39104.19 2 2


Capacitor 100 nF/250 V, G1 39105.18 1 1












What you need:

Complete Equipment Set, Manual on CD-ROM includedRLC Circuit P24406 01/11

2. Parallel-tuned circuit for

a) current resonance without par-allel resistor,

b) voltage resonance without par-allel resistor

c) voltage resonance with parallelresistor.


LEP_4 09.08.2007 11:55 Uhr Seite 187


Principle:The ripple of the output voltage ofvarious rectifier circuits is measuredas a function of the load currentstrength and the charging capaci-tance. The characteristics of a volt-age stabilizer and of a multiplier areinvestigated.

Tasks:1. Using the half-wave rectifier:a) to display the output voltage

(without charging capacitor) onthe oscilloscope

b) to measure the diode current ID asa function of the output currentstrength Io (with the charging capacitor)

c) to measure the ripple componentUACpp of the output voltage as afunction of the output current (C = constant)

d) to measure the ripple as a functionof the capacitance (Io = constant)

e) to measure the output voltage Uoas a function of the input voltageUi (Io = 0).

2. Using the bridge rectifier:a) to display the output voltage

(without charging capacitor) onthe oscilloscope

Ripple of the output voltage as a function of the charging current:a) half-wave rectifier, b) bridge rectifier.

b) to measure the current throughone diode, ID, as a function of theoutput current Io (with the charg-ing capacitor)

c) to measure the ripple of the out-put voltage as a function of theoutput current (C = constant)

d) to measure the ripple as a functionof the capacitance (Io = constant)

e) to measure the output voltage asa function of the input voltage.

3. To measure the voltage at thecharging capacitor, Uc, and theoutput voltage of a stabilizedvoltage source as a function ofthe input voltage Ui.

4. To measure the output voltage ofa voltage multiplier circuit as afunction of the input voltage.


� Half-wave rectifier� Full-wave rectifier� Graetz rectifier� Diode and Zener diode� Avalanche effect� Charging capacitor� Ripple� r.m.s. value� Internal resistance� Smoothing factor� Ripple voltage� Voltage stabilisation� Voltage doubling


Silicon diode 1 N 4007, G1 39106.02 4

Electrolyte capacitors, G1, 470 µF 39105.26 1

Electrolyte capacitors G1, 10 µF 39105.28 4

Electrolyte capacitors, G2, 2200 µF 39113.08 1

Electrolyte capacitors G1, 1000 µF 06049.09 1



Siliziumdiode ZF 4.7, G1 39132.01 1

Multi-tap transformer with rectifier 14 VAC/12 VDC, 5 A 13533.93 1



Rheostats, 330 Ω, 1.0 A 06116.02 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedRectifier circuits P2440700



LEP_4 09.08.2007 11:55 Uhr Seite 188



RC Filters 4.4.08-00

Principle:The frequency response of simple RCfilters is recorded by point-by-pointmeasurements and the sweep dis-played on the oscilloscope.

Tasks:To record the frequency response ofthe output voltage of

1. a high-pass filter

2. a low-pass filter

3. a band-pass filter

4. a Wien-Robinson bridge

5. a parallel-T filter,

point by point and to display thesweep on the oscilloscope.

Frequency response of high-pass and low pass filter.

To investigate the step response of

6. a differentiating network

7. an integrating network


Resistor 500 Ω 2%, 1W, G1 06057.50 1

Capacitor 10 nF/ 250 V, G1 39105.14 4

Carbon resistor 1kΩ, 1W, G1 39104.19 5



Wobble-functiongenerator 1 Hz-10 MHz 11766.95 1






Screened cable, BNC, l = 30 cm 07542.10 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedRC Filters P2440800


� High-pass� Low-pass� Wien-Robinson bridge� Parallel-T filters� Differentiating network� Integrating network� Step response� Square wave� Transfer function

LEP_4 09.08.2007 11:55 Uhr Seite 189


Principle:A coil, a capacitor, an ohmic resis-tance and combinations of thesecomponents are investigated fortheir filter characteristics as a func-tion of frequency. The phase dis-placement of the filters is deter-mined also as a function of frequen-cy.

Tasks:Determination of the ratio of outputvoltage to input voltage with the

1. RC/CR network,

2. RL/LR network,

3. CL/LC network,

4. Two CR networks connected inseries.

U/U1 as a function of the frequency with the LC and CL network.

5. Determination of the phase dis-placement with the RC/CR net-work.

6. Determination of the phase dis-placement with two CR networksconnected in series.


� Circuit� Resistance� Capacitance� Inductance� Capacitor� Coil� Phase displacement� Filter� Kirchhoff’s laws� Bode diagram








Coil, 300 turns 06513.01 1 1


Carbon resistor 1 kΩ, 1W, G1 39104.19 2 2














What you need:

Complete Equipment Set, Manual on CD-ROM includedHigh-pass and low-pass filters P24409 01/15




LEP_4 09.08.2007 11:55 Uhr Seite 190



RLC measuring bridge 4.4.10-00

Principle:Ohmic resistances, inductances andcapacitances are determined in aWheatstone bridge circuit operatedon AC. Balancing is done aurallythrough headphones, using the highsensitivity of the human ear.

Wheatstone bridge.

Tasks:To determine

1. ohmic resistances

2. inductances

3. capacitances

with the Wheatstone bridge, usingbridge balancing.

Simple slide wire measuring bridge 07182.00 1

Head phones, stereo 65974.00 1


Coil, 6 turns 06510.00 1

Coil, 300 turns 06513.01 1

Coil, 600 turns 06514.01 1

Coil, 1200 turns 06515.01 1

Coil, 600 turns, short 06522.01 1

Induction coil, 300 turns, d = 40 mm 11006.01 1



Carbon resistor G1, 680 Ω, 1 W 39104.17 1


Carbon resistor 1,5 kΩ, 1W, G1 39104.21 1



Potentiometer 100 Ω, 0.4W, G2 39103.01 1


Capacitor 100 pF/100 V, G2 39105.04 1

Capacitor 470 pF/100 V, G1 39105.07 1

Capacitor 1 nF/ 100 V, G2 39105.10 1

Capacitor 10 nF/ 250 V, G1 39105.14 1

Capacitor 47 nF/ 250 V, G2 39105.17 1

Capacitor 100 nF/250 V, G1 39105.18 1





Headphone Adapter jack plug/2 x 4 mm plug 65974.01 1

What you need:


� Wheatstone bridge� Inductive and capacitive

reactance� Ohmic resistance� Impedance� Kirchhoff’s laws

Complete Equipment Set, Manual on CD-ROM includedRLC measuring bridge P2441000

LEP_4 09.08.2007 11:55 Uhr Seite 191


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Z2

�2

Principle:Series circuits containing self-induc-tances or capacitances and ohmicresistances are investigated as afunction of frequency. Measuring theelectrical magnitudes with a work orpower measurement instrument, realpower or apparent power can be dis-played directly.

Tasks:1. Series circuit of self-inductanceand resistor (real coil)

– Investigation of impedance andphase shift as a function of fre-quency

– Investigation of the relation be-tween real power and current in-tensity

Capacitor and resistor in series, Z2 as a function of 1/f2.

– Determination of self-inductanceand ohmic resistance

2. Series circuit of capacitor and re-sistor

– Investigation of impedance and

phase shift as a function of fre-quency


� Impedance� Phase shift� Phasor diagram� Capacitance� Self-inductance

Work and power meter 13715.93 1


Coil, 300 turns 06513.01 1


Electrolyte capacitors non-polarised, G1, 47 µF 39105.45 1

Carbon resistor 10 Ohm, 1W, G1 39104.01 1

Connecting cable, 4 mm plug, 32 A, black, l = 50 cm 07361.05 4

What you need:

Complete Equipment Set, Manual on CD-ROM includedResistance, phase shift and powerin AC circuits P2441100



– Investigation of the relation be-tween real power and current in-tensity

– Determination of capacitance andohmic resistance

LEP_4 09.08.2007 11:55 Uhr Seite 192



Induction impulse 4.4.12-11

Principle:A permanent magnet falls with dif-ferent velocities through a coil. Thechange in the magnetic flux � gen-erates an induced voltage impulse.The induced voltage impulse USS isrecorded with a computer interfacesystem. Depending on the polarity ofthe permanent magnet the inducedvoltage impulse is negative or posi-tive.

Measured induction voltage USS versus time. Additionally the evaluation ofthe peak-to-peak voltage USS = 2.766 V is shown.

Tasks:1. Measurement of the induced volt-

age impulse USS and the fallingmagnet’s velocity.

2. Evaluation of the induced voltageimpulse USS as a function of themagnet’s velocity.

3. Calculation of the magnetic fluxinduced by the falling magnet as afunction of the magnet’s velocity.







Bosshead 02043.00 3



Glass tubes, AR-glass, d = 12 mm, l = 300 mm 45126.01 1

Coil holder 06528.00 1


Magnet, d = 8 mm, l = 60 mm 06317.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedInduction impulse P2441211


� Law of induction� Magnetic flux� Maxwell’s equations

LEP_4 09.08.2007 11:55 Uhr Seite 193

4.5.02-00 Coupled oscillating circuits

Principle:The Q factor of oscillating circuits isdetermined from the bandwidth andby the Pauli method. In inductivelycoupled circuits (band-pass filters)the coupling factor is determined asa function of the coil spacing.

Tasks:1. To determine the dissipation fac-

tor tan �k and the quality factorQ from the bandwidth of oscillat-ing circuits.

2. To determine the dissipation fac-tor and Q factor of oscillating cir-cuits from the resonant frequency

Coupling constant k as a function of the distance s between the coils whenthe coupling is supercritical.

(�0), the capacitance Ctot. and theparallel conductance Gp determinedby the Pauli method.

3. To determine the coupling factork and the bandwidth �f of aband-pass filter as a function ofthe coil spacing s.


� Resonance� Q factor� Dissipation factor� Bandwidth� Critical or optimum coupling� Characteristic impedance� Pauli method� Parallel conductance� Band-pass filter� Sweep

Wobble-functiongenerator 1 Hz-10 MHz 11766.95 1


HF coils, 35 turns; 75 µH 06915.00 2

HF coils, 50 turns, 150 µH 06916.00 2

HF coils, 75 turns, 350 µH 06917.00 2


Variable capacitor, Casing G3 06049.10 2




Carbon resistor 1 MΩ, 1W, G1 39104.52 2

Carbon resistor G1, 82 kΩ, 1 W 39104.40 1

Capacitor 470 pF/100 V, G2 39105.07 1



G-clamp 02014.00 2

Meter Scale, l = 1000 x 27 mm 03001.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedCoupled oscillating circuits P2450200


Electricity Electromagnetic Oscillations and Waves

LEP_4 09.08.2007 11:55 Uhr Seite 194


Electromagnetic Oscillations and Waves Electricity

Interference of microwaves 4.5.04-00

Principle:A microwave beam, after reflectionfrom a metal screen or glass plate,interferes with the primary waves.The wavelength is determined fromthe resultant standing waves.

Intensity distribution during interference of microwaves in the Michelsonarrangement, as a function of the position of the reflection screens.

Tasks:Measurement of the wavelength ofmicrowaves through the productionof standing waves with

1. reflection at the metal screen,

2. plane-parallel plate,

3. the Michelson interferometer.

Microwave transmitter with clystron 11740.01 1

Microwave receiver 11740.02 1

Microwave receiving dipole 11740.03 1

Microwave power supply, 220 VAC 11740.93 1


Glass plate, clear glass, 200 x 300 x 4 mm 08204.00 2



G-clamp 02014.00 2

Meter Scale, l = 1000 x 27 mm 03001.00 2









What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference of microwaves P2450400


� Wavelength� Standing wave� Reflection� Transmission� Michelson interferometer

LEP_4 09.08.2007 11:55 Uhr Seite 195


Principle:Microwaves impinge on a slit andthe edge of a screen. The diffractionpattern is determined on the basis ofdiffraction at these obstacles.

Intensity distribution in the diffraction of the microwaves at the edge of ascreen, parallel to the plane of the screen.

Tasks:Determination of the diffraction pat-tern of the microwave intensity

1. behind the edge of a screen,

2. after passing through a slit,

3. behind a slit of variable width,with a fixed receiving point.


� Fresnel zones� Huygens’ principle� Fraunhofer diffraction� Diffraction at the slit







Meter Scale, l = 1000 x 27 mm 03001.00 2





G-clamp 02014.00 2




What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction of microwaves P2450500



LEP_4 09.08.2007 11:55 Uhr Seite 196



Diffraction and polarization of microwaves 4.5.06-00

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-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

150

100

50

l = 20 cm

l = 40 cm

l = 30 cm

U in mV

l = W-Soin cm

with lens

without lens

Principle:The equivalence between visible lightand microwaves as special cases ofthe total spectrum of electromag-netic waves can be demonstratedusing diffraction and polarization ofmicrowaves as an example. Thefocusing of microwaves through aplane convex convergent lens isobserved and the focal distance ofthe lens is determined. After that,polarizability of microwaves is dem-onstrated by means of a metallicgrating.

Tasks:1. Measuring the irradiance of the

microwave field behind a conver-ging lens

– along the optical axis

– transversally to the optical axis.

Determination of the focal length ofa synthetic resin converging lens andcomparison of the results with the

Profile of the intensity of radiation.

distribution of irradiance when nolens is used.

2. Measurement of the irradiancetransmitted through a metal grat-ing as a function of the anglebetween the direction of polariza-tion and the grating bars.





Polarisation grid 06866.00 1

Convergent lens, synthetic resin 06872.00 1


Voltmeter 0.3...300 V-, 10...300 V~ 07035.00 1









H-base -PASS- 02009.55 1






Meter Scale, l = 1000 x 27 mm 03001.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction and polarization of microwaves P2450600


� Diffraction� Focal point� Linearity� Circularly and elliptically

polarized waves� Transverse waves� Polarizer and Analyzer� Constructive and destructive

interference

LEP_4 09.08.2007 11:55 Uhr Seite 197


x

xx

xx

x

x

x

xx x xxx

x

x x xx

xx

x

x

x

x

r = 60 cm

0,5

� = 45°1--4

0 30 60– 60 – 30 = 00in

U–Umax

r = 20 cm

1

Principle:The directional characteristic of ahorn antenna is received in two per-pendicular planes by means of areceiving dipole. The law of distancefor the antenna is verified.

Directional characteristic Cu(, = 0) of the horn antenna in the polariza-tion plane for different distances.

Tasks:1. Measurement of the directional

characteristic of the horn antennain two perpendicular planes andevaluation of the correspondingdirectivity from the directionalcharacteristic.

2. Determination of the microwaveirradiance I as a function of thedistance r between the receivingdipole and the horn antenna,which verifies the validity of thelaw.


� Horn antenna� Directional characteristic

pattern� Directivity� Law of distance� Phase center











Graduated disk, for demonstration 02053.02 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedRadiation field of a horn antenna /Microwaves P2450800



LEP_4 09.08.2007 11:55 Uhr Seite 198



Frustrated total reflection / Microwaves 4.5.09-00

k1

k2

n1

n2

n1

k1

x

y

kr

�

�

�

�

Principle:In the first part, the transmission andreflection characteristics of glass,acrylic glass and metal are studiedwith a microwave transmitter-receiver pair and are compared toeach other.

In the second part, total reflection ofmicrowaves on a prismatic surface issuppressed by bringing a secondprism with the same refractive indexclose to the first one.

Frustrated total internal reflection.

Tasks:1. Determination of the reflecting

and transmitting characteristics ofglass, acrylic glass and metal.

2. Observation of the effect of frus-trated total reflection and deter-mination of the transmitted irra-diance as a function of distance dto the prismatic surface. Therefractive index of the prismmaterial can be calculated bydetermining the attenuation coef-ficient �.





Glass plate, clear glass, 200 x 300 x 4 mm 08204.00 1

Plexiglas plate 200 x 200 x 4 mm 11613.00 1



Supporting block 105 x 10 5x 57 mm 02073.00 2

Prism, synthetic resin 06873.00 2




Vernier caliper, plastic 03011.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFrustrated total reflection / Microwaves P2450900


� Transmission� Reflection� Absorption� Refraction� Phase velocity� Total reflection� Surface waves� Frustrated total reflection� Tunnel effect

LEP_4 09.08.2007 11:55 Uhr Seite 199


Electricity Handbooks

36 described Experiments

Please ask for a complete equipmentlist Ref. No. 24510

1 Electric Circuits1.1 (13801)The simple circuit

1.2 (13802)Measurement of voltage

1.3 (13803)Measurement of current

1.4 (13804)Conductors and non-conductors

1.5 (13805)Changeover switches and alternateswitches

1.6 (13806)Parallel and series connection of voltagesources

1.7 (13807)The safety fuse

1.8 (13808)The bimetallic switch

1.9 (13809)AND and OR Circuits

2 Electrical Resistance2.1 (13810)Ohm’s Law

2.2 (13811)The resistance of wires – dependence onlength and cross-section

2.3 (13812)The resistance of wires – dependence onmaterial and temperature

2.4 (13813)The resistivity of wires

2.5 (13814)Current strength and resistance with resist. connec. in parallel

2.6 (13815)Current strength and resistance with resist. connec. in series

2.7 (13816)Voltage in a series connection

2.8 (13817)The potentiometer

2.9 (13818)The internal resistance of a voltagesource

3 Electric Power and Work3.1 (13819)The Power and work of electric current

4 Capacitors4.1 (13820)Capacitors in direct current circuits

4.2 (13821)The charging and discharging of a capacitor

4.3 (13822)Capacitors in alternating current circuits

5 Diodes, Part 15.1 (13823)The diode as electrical valve

5.2 (13824)The diode as rectifier

5.3 (13825)The characteristic curve of a silicondiode

5.4 (13826)Properties of solar cells – the depen-dence on the illuminating intensity

5.5 (13827)The characteristic current-voltage curvesof a solar cell

5.6 (13828)Solar cells connected in series and inparallel – characteristic current-voltagecurves and performance

5.7 (13829)Series and parallel connections of solarcells – characteristic current-voltagecurves and power

5.8 (13830)The characteristic curve of a germaniumdiode

6 Transistors, Part 16.1 (13831)The npn transistor

6.2 (13832)The transistor as direct current amplifier

6.3 (13833)The characteristic current-voltage curvesof a transistor

6.4 (13834)The transistor as a switch

6.5 (13835)The transistor as a time-delay switch

6.6 (13836)The p-n-p transistor



7 Transformation of energy7.1 (13967)The transformation of electrical energyinto heat energy7.2 (13968)The transform. of electrical energy intomechanical energy

8 Electrochemistry8.1 (13969)The conductivity of electrolytes8.2 (13970)Voltage and current strength in conductive processes in liquids8.3 (13971)Electrolysis8.4 (13972)Galvanization8.5 (13973)Galvanic cells8.6 (13974)The lead accumulator8.7 (13975)The PEM Electrolyser and PEM Fuel cell8.8 (13976)The PEM Solar-hydrogen model

9 Electromagnetism9.1 (13977)The magnetic effect of a current-carrying conductor9.2 (13978)Lorentz force: A current-carryingconductor in a mag. field9.3 (13979)The electric bell9.4 (13980)A model of an electromagnetic relay9.5 (13981)Controlling with a relay9.6 (13982)The twilight switch9.7 (13983)The galvanometer9.8 (13984)The reed switch

10 Electric motors10.1 (13985)The permanent magnet motor10.2 (13986)The main circuit motor10.3 (13987)The shunt motor10.4 (13988)The synchronous motor

11 Induction11.1 (13989)Induction voltage with a permanentmagnet11.2 (13990)Induction voltage with an electromagnet11.3 (13991)The alternating current generator11.4 (13992)The direct current generator11.5 (13993)Lenzsche’s rule11.6 (13994)The behaviour of a direct current generator under load

12 Transformers12.1 (13995)Voltage transformation

12.2 (13996)Current transformation12.3 (13997)Forces between primary and secondarycoils12.4 (13998)The heavy current transformer

13 Self-induction13.1 (13999)Self-induction on switching on13.2 (14000)Self-induction on switching off13.3 (14001)Coils in alternating current circuits13.4 (14002)Current strength on switching coils onand off

14 Safe working with electrical energy14.1 (14003)Earthing of the power supply line14.2 (14004)The protective conductor system14.3 (14005)The protective break transformer

15 Sensors15.1 (14006)The NTC resistor15.2. (14007)The PTC resistor15.3 (14008)The light dependent resistor (LDR)

16 Diodes, Part 216.1 (14009)The characteristic curve of a Z-diode16.2 (14010)The Z-diode as voltage stabilizer16.3 (14011)The light emitting diode16.4 (14012)The photo diode16.5 (14013)The bridge rectifier16.6 (14014)The filter network

17 Transistors, Part 217.1 (14015)Voltage amplification of a transistor17.2 (14016)Stabilization of the operating point17.3 (14017)Transistor control with light17.4 (14018)Temperature control of a transistor17.5 (14019)Undamped electromagnetic oscillations17.6 (14020)Transistors in a digital circuit 17.7 (14021)The Darlington circuit17.8 (14022)How phototransistors function17.9 (14023)Information transfer through a photoconductor

18 The operational amplifier and applications

18.1 (14024)The differential amplifier18.2 (14025)The digital circuit18.3 (14026)The generation of oscillations

Demonstration Experiments Physics – Electricity /Electronics on the Magnetic Board 1+ 2

Electricity/Electronics on the Magnetic Board 1 • No. 01001.02

Electricity/Electronics on the Magnetic Board 2 • No. 01003.02

LEP_4 09.08.2007 11:55 Uhr Seite 200

5Physical Structureof Matter

LEP_5_1 09.08.2007 12:13 Uhr Seite 201


Contents

5.1 Physics of the Electron5.1.01-00 Elementary charge and Millikan experiment


5.1.03-11 Franck-Hertz experiment with Hg-tube


5.1.04-01/05 Planck’s “quantum of action” from photoelectric effect (line separation by interference filters)

5.1.05-01/05 Planck’s “quantum of action” from the photoelectric effect (line separation by defraction grating)

5.1.06-00 Fine structure, one-electron and two-electron spectra


5.1.08-00 Atomic spectra of two-electron systems: He, Hg

5.1.10-05 Zeeman effect

5.1.11-01/11 Stern-Gerlach experiment


5.1.13-00 Electron diffraction

5.2 Radioactivity5.2.01-01 Half-life and radioactive equilibrium

5.2.01-11 Half-life and radioactive equilibrium with Cobra3

5.2.03-11 Poisson’s distribution and Gaussian distribution of radioactive decay with Cobra3 – Influence of the dead time of the counter tube

5.2.04-00 Visualisation of radioactive particles / Diffusion cloud chamber

5.2.20-15 Alpha-Energies of different sources with Multi Channel Analyzer

5.2.21-01/11/15 Rutherford experiment


5.2.23-01/11/15 Study of the �-energies of 226Ra


5.2.31-00 Electron absorption


5.2.41-01/11 Law of distance and absorption of gamma or beta rays

5.2.42-01/11/15 Energy dependence of the �-absorption Coefficient

5.2.44-01/11/15 Compton effect


5.2.46-01/11/15 Photonuclear cross-section / Compton scattering cross-section


5.3 Solid-state Physics, Plasma Physics5.3.01-01 Hall effect in p-germanium


5.3.02-01/11 Hall effect in n-germanium


5.3.04-01 Band gap of germanium


Physical Structure of Matter

5.3.10-00 Surface treatment / Plasma Physics5.3.11-00 Paschen curve / Plasma Physics

5.4 X-ray Physics5.4.01-00 Characteristic X-rays of copper5.4.02-00 Characteristic X-rays of molybdenum5.4.03-00 Characteristic X-rays of iron5.4.04-00 The intensity of characteristic X-rays as a function of anode

current and anode voltage5.4.05-00 Monochromatization of molybdenum X-rays5.4.06-00 Monochromatization of copper X-rays5.4.07-00 K� doublet splitting of molybdenum X-rays / fine structure5.4.08-00 K� doublet splitting of iron X-rays / fine structure5.4.09-00 Duane-Hunt displacement law and Planck's “quantum of action”5.4.10-00 Characteristic X-ray lines of different anode materials /

Moseley's Law; Rydberg frequency and screening constant5.4.11-00 Absorption of X-rays5.4.12-00 K- and L-absorption edges of X-rays /

Moseley's Law and the Rydberg constant5.4.13-00 Examination of the structure of NaCl monocrystals with differ-

ent orientations5.4.14/15-00 X-ray investigation of different crystal structures /

Debye-Scherrer powder method5.4.16-00 X-ray investigation of crystal structures / Laue method5.4.17-00 Compton scattering of X-rays5.4.18-00 X-ray dosimetry5.4.19-00 Contrast medium experiment with a blood vessel model5.4.20-00 Determination of the length and position of an object which

cannot be seen5.4.21-00 Diffractometric Debye-Scherrer patterns of powder samples

with the three cubic Bravais lattices5.4.22-00 Diffractometric Debye-Scherrer patterns of powder samples

with diamond structure (germanium and silicon)5.4.23-00 Diffractometric Debye-Scherrer patterns of powder samples

with a hexagonal lattice structure5.4.24-00 Diffractometric Debye-Scherrer patterns of powder samples

with a tetragonal lattice structure5.4.25-00 Diffractometric Debye-Scherrer patterns of powder samples

with a cubic powder sample5.4.26-00 Diffractometric measurements to determine the intensity of

Debye-Scherrer reflexes using a cubic lattice powder sample5.4.27-00 Diffractometric Debye-Scherrer measurements

for the examination of the texture of rolled sheets5.4.28-00 Characteristic X-rays of tungsten 5.4.40-00 Spectroscopy with the X-ray energy detector

6.4 HandbooksX-Ray ExperimentsInterface-System Cobra3 Physics, Chemistry/Biology

5LEP_5_1 09.08.2007 12:13 Uhr Seite 202


Elementary charge and Millikan experiment 5.1.01-00

Physics of the Electron Physical Structure of Matter

1,20E-18

1,00E-18

8,00E-19

6,00E-19

4,00E-19

2,00E-19

0,00E+000,00E+00

2,00E-07 4,00E-07 6,00E-07 8,00E-07 1,00E-07 1,20E-07

r/m

Q/A

s

Principle:Charged oil droplets subjected to anelectric field and to gravity betweenthe plates of a capacitor are acceler-ated by application of a voltage. Theelementary charge is determinedfrom the velocities in the direction ofgravity and in the opposite direction.

Tasks:1. Measurement of the rise and fall

times of oil droplets with variouscharges at different voltages.

2. Determination of the radii and thecharge of the droplets.

Measurements on various droplets for determining the elementary charge bythe Millikan method.


� Electric field� Viscosity� Stokes’ law� Droplet method� Electron charge

Millikan apparatus 09070.00 1

Multi-range meter, with overl. prot. 07021.01 1

Power supply, 0...600 VDC 13672.93 1

Object micrometer 1 mm i.100 parts 62171.19 1

Stopwatch, interruption type 03076.01 2

Cover glasses, 18 x 18 mm, pack of 50 pcs. 64685.00 1

Polarity Switch for Millikan Apparatus 06034.07 1



Circular level 02122.00 1

Connecting cord, safety, 32 A, 50 cm, red 07336.01 1

Connecting cord, safety, 32 A,100 cm, red 07337.01 2

Connecting cord, safety, 32 A,100 cm, blue 07337.04 2

Connecting cord, 32 A, 750 mm, black 07362.05 2

Connecting cord, 32 A, 750 mm, green-yellow 07362.15 1

Optional accessories:

Radioactive source, Am-241, 74 kBq 09047.51 1

Circular level 02122.00 1

FlexCam Scientific Pro II 88030.93 1

TV set

What you need:

Complete Equipment Set, Manual on CD-ROM includedElementary charge and Millikan experiment P2510100

LEP_5_1 09.08.2007 12:13 Uhr Seite 203



Principle:Electrons are accelerated in anelectric field and enter a magneticfield at right angles to the directionof motion. The specific charge of theelectron is determined from theaccelerating voltage, the magneticfield strength and the radius of theelectron orbit.

Tasks:Determination of the specific chargeof the electron (e/m0) from the pathof an electron beam in crossedelectric and magnetic fields of vari-able strength.

Narrow beam tube with socket 06959.00 1










What you need:

Complete Equipment Set, Manual on CD-ROM includedSpecific charge of the electron – e/m P2510200

Physical Structure of Matter Physics of the Electron


� Cathode rays� Lorentz force� Electron in crossed fields� Electron mass� Electron charge

LEP_5_1 09.08.2007 12:13 Uhr Seite 204


Franck-Hertz experiment with Hg-tube 5.1.03-11


Principle:Electrons are accelerated in a tubefilled with mercury vapour.

The excitation energy of mercury isdetermined from the distance be-tween the equidistant minima of theelectron current in a variable oppos-ing electric field.

Example of a Franck-Hertz curve for Hg-gas recorded with T = 180°C.

Tasks:1. Record the counter current

strength Is in a Franck-Hertz tubeas a function of the anode voltageUa.

2. To determine the excitation ener-gy Ea from the positions of thecurrent strength minima or maxi-ma by difference formation.


� Energy quantum� Electron collision� Excitation energy

Franck-Hertz control unit 09105.99 1

Franck-Hertz Hg-tube on plate 09105.10 1

Franck-Hertz oven for Hg-tube 09105.93 1

Thermocouple NiCr-Ni, sheathed 13615.01 1

Connecting cable for Franck-Hertz Hg-tube 09105.30 1



Software Measure Franck-Hertz experiment 14522.61 1


Optional equipment:

Oscilloscope, 30 MHz, 2 channels 11459.95 1

Adapter, BNC-socket/4mm plug pair 07542.27 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedFranck-Hertz experiment with Hg-tube P2510311

LEP_5_1 09.08.2007 12:13 Uhr Seite 205



Principle:Electrons are accelerated in a tubefilled with neon vapour.

The excitation energy of neon is de-termined from the distance betweenthe equidistant minima of the elec-tron current in a variable opposingelectric field.

Example of a Franck-Hertz curve for Ne-gas.

Tasks:1. Record the counter current

strength Is in a Franck-Hertz tubeas a function of the anode voltageUa.

2. To determine the excitation ener-gy Ea from the positions of thecurrent strength minima or maxi-ma by difference formation.

Franck-Hertz control unit 09105.99 1

Franck-Hertz Ne-tube with housing 09105.40 1

Connecting cable for Franck-Hertz Ne-tube 09105.50 1



Software Measure Franck-Hertz experiment 14522.61 1


Optional equipment:

Oscilloscope, 30 MHz, 2 channels 11459.95 1

Adapter, BNC-socket/4mm plug pair 07542.27 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedFranck-Hertz experiment with Ne-tube P2510315



� Energy quantum� Quantum leap� Electron collision� Excitation energy

LEP_5_1 09.08.2007 12:13 Uhr Seite 206


Planck’s “quantum of action” from the photoelectric effect 5.1.04-01/05(line separation by interference filters)


Principle:A photo-cell is illuminated with lightof different wavelengths. Planck’squantum of action, or Planck’s con-stant (h), is determined from thephotoelectric voltages measured.

Voltage of the photo-cell as a function of the frequency of the irradiatedlight.

Tasks:To determine Planck’s quantum ofaction from the photoelectric volt-ages measured at different wave-lengths.


� External photoelectric effect� Work function� Absorption� Photon energy� Anode� Cathode

Experiment P2510405 with electrometerExperiment P2510401 with amplifier

Photocell, for h detection, with housing 06778.00 1 1

Interference filters, set of 3 08461.00 1 1

Interference filters, set of 2 08463.00 1 1

Experiment lamp 6 11615.05 1 1

Spectral lamp Hg 100, pico 9 base 08120.14 1 1

Power supply for spectral lamps 13662.97 1 1



Screened cable, BNC, l = 30 cm 07542.10 1 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedPlanck’s “quantum of action” from the photoelectriceffect (line separation by interference filters) P25104 01/05

Set-up of experiment P2510405 with electrometer

LEP_5_1 09.08.2007 12:13 Uhr Seite 207


5.1.05-01/05 Planck’s “quantum of action” from the photoelectric effect(line separation by defraction grating)

Principle:A photocell is illuminated withmonochromatic light of differentwavelengths. Planck’s quantum ofaction, or Planck’s constant h, isdetermined from the photoelectricvoltages measured.

Voltage of the photo-cell as a function of the frequency of the irradiatedlight.

Experiment P2510505 with electrometerExperiment P2510501 with amplifier

Photocell, for h detection, with housing 06778.00 1 1

Diffraction grating, 600 lines/mm 08546.00 1 1

Colour filter, 580 nm 08415.00 1 1

Colour filter, 525 nm 08414.00 1 1

Diaphragm holder, attachable 11604.09 2 2

Slit, adjustable 08049.00 1 1

Lens holder 08012.00 2 2

Lens, mounted, f = +100 mm 08021.01 1 1

Mercury vapour high pressure lamp, 80 W 08147.00 1 1

Screened cable, BNC, l = 30 cm 07542.10 1 1



Lamp socket E 27 on stem 06176.00 1 1

Power supply for spectral lamps 13662.97 1 1



Optical profile bench, l = 600 mm 08283.00 2 2

Base for optical profile bench, adjustable 08284.00 3 3

Turning knuckle for optical profile bench 08285.00 1 1

Slide mount for optical profil bench, h = 80 mm 08286.02 4 4




What you need:

Complete Equipment Set, Manual on CD-ROM includedPlanck’s “quantum of action” from the photoelectriceffect (line separation by defraction grating) P25105 01/05



� External photoelectric effect� Work function� Adsorption� Photon energy

Set-up of experiment P2510501 with amplifier

LEP_5_1 09.08.2007 12:13 Uhr Seite 208


Fine structure, one-electron and two-electron spectra 5.1.06-00


Principle:The well-known spectral lines of Heare used for calibrating the diffrac-tion spectrometer. The wave-lengthsof the spectral lines of Na, Hg, Cdand Zn are determined using thespectrometer.

Spectrum of sodium.

Tasks:1. Calibration of the spectrometer

using the He spectrum, and thedetermination of the constant ofthe grating;

2. Determination of the spectrum ofNa;

3. Determination of the fine struc-ture splitting.

4. Determination of the most intensespectral lines of Hg, Cd and Zn.


� Diffraction spectrometer� Spin� Angular momentum� Spin-orbital angular

momentum interaction� Multiplicity� Energy level� Excitation energy� Selection rules� Doublets� Parahelium� Orthohelium� Exchange energy� Angular momentum� Singlet and triplet series� Selection rules� Forbidden transition

Spectrometer/goniometer with verniers 35635.02 1


Spectral lamp He, pico 9 base 08120.03 1

Spectral lamp Na, pico 9 base 08120.07 1


Spectral lamp Cd, pico 9 base 08120.01 1

Spectral lamp Zn, pico 9 base 08120.11 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedFine structure, one-electron and two-electron spectra P2510600

LEP_5_1 09.08.2007 12:13 Uhr Seite 209




Brackett-Series

Paschen-Series

Balmer-Series

Lyman-Series

ener

gy le

vel

ioni

zatio

n en

ergy

13.

6 eV

eV

0

–0.9

–1.5

–3.4

–13.6 n = 1

n = 2

n = 3

n = 4

n = �

H�

H�

H�

H�

H�

Principle:The spectral lines of hydrogen andmercury are examined by means of adiffraction grating. The known spec-tral lines of Hg are used to determinethe grating constant. The wavelengths of the visible lines of theBalmer series of H are measured.

Energy level diagram of the H atom.

Tasks:1. Determination of the diffraction

grating constant by means of theHg spectrum.

2. Determination of the visible linesof the Balmer series in the H spec-trum, of Rydberg’s constant and ofthe energy levels.

Spectral tube, H2 06665.00 1

Spectral tube, Hg 06664.00 1

Holders for spectral tubes, 1 pair 06674.00 1

Cover tube for spectral tubes 06675.00 1











Meter Scale, l = 1000 x 27 mm 03001.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedBalmer series / Determination of Rydberg’s constant P2510700


� Diffraction image of adiffraction grating

� Visible spectral range� Single electron atom� Atomic model according

to Bohr� Lyman-, Paschen-, Brackett-

and Pfund-Series� Energy level� Planck’s constant� Binding energy

LEP_5_1 09.08.2007 12:13 Uhr Seite 210


Atomic spectra of two-electron systems: He, Hg 5.1.08-00


Principle:The spectral lines of He and Hg areexamined by means of a diffractiongrating. The wavelengths of the linesare determined from the geometricalarrangement and the diffractiongrating constants.

Measured spectral lines of He/Hg and the corresponding energy-level transi-tions.

Tasks:1. Determination of the wavelengths

of the most intense spectral linesof He.

2. Determination of the wavelengthsof the most intense spectral linesof Hg.


� Parahelium� Orthohelium� Exchange energy� Spin� Angular momentum� Spinorbit interaction� Singlet and triplet series� Multiplicity� Rydberg series� Selection rules� Forbidden transition� Metastable state� Energy level� Excitation energy

Spectral tube, Hg 06664.00 1

Spectral tube, He 06668.00 1

Holders for spectral tubes, 1 pair 06674.00 1

Cover tube for spectral tubes 06675.00 1











Meter Scale, l = 1000 x 27 mm 03001.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedAtomic spectra of two-electron systems: He, Hg P2510800

Colour �/nm Transition

red 665 ± 2 3 1D R 2 1P

yellow-orange 586 ± 2 3 3D R 2 3P

green 501 ± 2 3 1D R 2 1P

blue-green 490 ± 2 4 1D R 2 1P

blue 470 ± 3 4 3S R 2 3P

violet 445 ± 1 4 3D R 2 3P

Colour �/nm Transition

yellow 581 ± 1 { 6 1D1 R 6 1P16 3D1 R 6 1P1

green 550 ± 1 7 3S1 R 6 3P1

green 494 ± 2 8 1S1 R 6 1P1

blue 437 ± 2 7 1S R 6 1P1

LEP_5_1 09.08.2007 12:13 Uhr Seite 211



5.1.10-05 Zeeman effect /normal and anomalous version

Principle:The “Zeeman effect” is the splittingof the spectral lines of atoms withina magnetic field. The simplest is thesplitting up of one spectral line intothree components called “normalZeeman effect”. Usualy the phe-nomenon is more complex and thecentral line splits into many morecomponents. This is the “anomalousZeeman effect”. Both effects can bestudied using a cadmium lamp as aspecimen. The cadmium lamp is sub-mitted to different magnetic fluxdensities and the splitting of the redcadmium line (normal Zeeman effect)and that of a green cadmium line

Tasks:1. Using the Fabry-Perot interfero-

meter and a self made telescopethe splitting up of the central linesinto different lines is measured inwave numbers as a function of themagnetic flux density.

2. From the results of point 1. a valuefor Bohr’s magneton is evaluated.

3. The light emitted within thedirection of the magnetic field isqualitatively investigated.

Interference rings with the anomalous Zeeman effect.

(anomalous Zeeman effect) is inves-tigated using a Fabry-Perot interfer-ometer. The evaluation of the resultsleads to a fairly precise value forBohr’s magneton.

Fabry-Perot interferometer 09050.02 1Cadmium lamp for Zeeman effect 09050.01 1Electromagnet without pole shoes 06480.01 1Pole pieces, drilled, conical, 1 pair 06480.03 1Rotating table for heavy loads 02077.00 1Power supply for spectral lamps 13662.97 1Variable transformer 25 V~/20 V- , 12 A 13531.93 1Electrolyte capacitor, 22000 µF 06211.00 1Digital multimeter 2010 07128.00 1Optical profile bench, l = 1000 mm 08282.00 1Base for optical profile bench, adjustable 08284.00 2Slide mount for optical profil bench, h = 30 mm 08286.01 5Slide mount for optical profil bench, h = 80 mm 08286.02 2Lens holder 08012.00 4Lens, mounted, f = +50 mm 08020.01 2Lens, mounted, f = +300 mm 08023.01 1Iris diaphragm 08045.00 1Polarisation filter on stem 08610.00 1Polarisation specimen, mica 08664.00 1Connecting cable, 4 mm plug, 32 A, red, l = 25 cm 07360.01 1Connecting cable, 4 mm plug, 32 A, blue, l = 25 cm 07360.04 1Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 1Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 1Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 1Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 1Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 1CCD-camera for PC-use, USB* 88037.00 1

PC with USB interface, Windows 98SE/Windows Me/Windows 2000/Windows XP

*Alternative to CCD-Camera incl. measurement software, two slide mounts,h = 80 mm for classical version of the Zeeman Effect:Slide mount for optical profile-bench, 08286.00 1Sliding device, horizontal 08713.00 1Swinging arm 08256.00 1

What you need:


� Bohr’s atomic model� Quantisation of energy levels� Electron spin� Bohr’s magneton� Interference of

electromagnetic waves� Fabry-Perot interferometer

Plate holder with tension spring 08288.00 1Screen, with aperture and scale 08340.00 1Slide mount for opt. profile-bench, h = 80 mm 08286.02 1

Complete Equipment Set, Manual on CD-ROM includedZeeman effect /normal and anomalous version P2511005

LEP_5_1 09.08.2007 12:13 Uhr Seite 212


Stern-Gerlach experiment 5.1.11-01/11


Principle:A beam of potassium atoms generat-ed in a hot furnace travels along aspecific path in a magnetic two-wirefield. Because of the magnetic mo-ment of the potassium atoms, thenonhomogeneity of the field appliesa force at right angles to the direc-tion of their motion. The potassiumatoms are thereby deflected fromtheir path.

By measuring the density of thebeam of particles in a plane of de-tection lying behind the magnetic

field, it is possible to draw conclu-sions as to the magnitude and direc-tion of the magnetic moment of thepotassium atoms.

Tasks:1. Recording the distribution of the

particle beam density in the de-tection plane in the absence of theeffective magnetic field.

2. Fitting a curve consisting of astraight line, a parabola, and an-other straight line, to the experi-

Ionization current as a function of position (u) of detector with large excita-tion currents in the magnetic analyser.

mentally determined special distri-bution of the particle beam density.

3. Determining the dependence ofthe particle beam density in thedetection plane with different val-ues of the non-homogeneity ofthe effective magnetic field.

4. Investigating the positions of themaxima of the particle beam den-sity as a function of the non-ho-mogeneity of the magnetic field.


� Magnetic moment� Bohr magneton� Directional quantization� g-factor� Electron spin� Atomic beam� Maxwellian velocity

distribution� Two-wire field

Experiment P2511111 with PC interfaceExperiment P2511101 classicalStern-Gerlach apparatus 09054.88 1 1Matching transformer 09054.04 1 1Potassium ampoules, set of 6 09054.05 1 1High vacuum pump assembly, compact 09059.99 1 1Electromagnet without pole shoes 06480.01 1 1Pole piece, plane 06480.02 2 2Commutator switch 06034.03 1 1Voltmeter 0.3...300 V-, 10...300 V~ 07035.00 2 1Ammeter, 1 mA...3 A DC/AC 07036.00 2 2Meter 10/30 mV, 200°C 07019.00 1 1Storage tray, 413 x 240 x 100 mm 47325.02 1 1Crystallizing dishes, BORO 3.3., 2300 ml 46246.00 1 1Isopropyl alcohol, 1000 ml 30092.70 1 1Direct current measuring amplifier 13620.93 1 1Variable transformer with rectifier 15 V~/12 V- , 5 A 13530.93 1 1Power supply 0-12 V DC/ 6 V, 12 V AC 13505.93 2 2Two tier platform support 02076.03 1 1Rubber tubing/vacuum, d = 6 mm 39286.00 3 3Connecting cable, 4 mm plug, 32 A, yellow, l = 25 cm 07360.02 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 25 cm 07360.04 2 2Connecting cable, 4 mm plug, 32 A, red, l = 50 cm 07361.01 3 2Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm 07361.04 2 1Connect. cable, 4 mm plug, 32 A, green-yellow, l = 50 cm 07361.15 1 1Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 1 1Connecting cable, 4 mm plug, 32 A, yellow, l = 75 cm 07362.02 3 3Steel cylinders, nitrogen, 10 l 41763.00 1 1Pressure-reducing valves, nitrogen 33483.00 1 1Gas-cylinder Trolley for 10 l 41790.10 1 1Step motor Stern-Gerlach appartus 09054.06 1Step motor unit 08087.99 1Data cable USB, plug type A/B, l = 1.8 m 14608.00 1Software for stepping motor 14451.61 1Adapter, BNC-socket/4 mm plug pair 07542.27 1Screened cable, BNC, l = 1500 mm 07542.12 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedStern-Gerlach experiment P2511101/11

Set-up of experiment P2511111 with PC interface

LEP_5_1 09.08.2007 12:13 Uhr Seite 213



Principle:The g-factor of a DPPH (Diphenyl-pikrylhydrazyl) and the half-width ofthe absorption line are determined,using the ESR apparatus.

Electron spin resonance (ESR), model experiment.

Tasks:With ESR on a DPPH specimen deter-mination of

1. the g-factor of the free electron,and

2. the half-width of the absorptionline.

ESR resonator with field coils 09050.00 1

ESR power supply 09050.93 1



Digital Mulitmeter 2010 07128.00 1






Options:


Hall probe, tangential, protective cap 13610.02 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedElectron spin resonance P2511200



� Zeeman effect� Energy quantum� Quantum number� Resonance� g-factor� Landé factor

LEP_5_1 09.08.2007 12:13 Uhr Seite 214


Electron diffraction 5.1.13-00


Principle:Fast electrons are diffracted from apolycrystalline layer of graphite: in-terference rings appear on a fluores-cent screen. The interplanar spacingin graphite is determined from thediameter of the rings and the accel-erating voltage.

Tasks:1. To measure the diameter of the

two smallest diffraction rings atdifferent anode voltages.

2. To calculate the wavelength of theelectrons from the anode voltages.

3. To determine the interplanar spac-ing of graphite from the relation-ship between the radius of thediffraction rings and the wave-length.


� Bragg reflection� Debye-Scherrer method� Lattice planes� Graphite structure� Material waves� De Broglie equation

Electron diffraction tube on mounting 06721.00 1












What you need:

Complete Equipment Set, Manual on CD-ROM includedElectron diffraction P2511300

LEP_5_1 09.08.2007 12:13 Uhr Seite 215


5.2.01-01 Half-life and radioactive equilibrium

Principle:The half-life of a Ba-137 m daughtersubstance eluted (washed) out of aCa-137 isotope generator is meas-ured directly and is also determinedfrom the increase in activity afterelution.

Tasks:1. To record the counting rate as a

function of the counter tube volt-age (counter tube characteristic)when the isotope generator activ-ity is constant (radioactive equi-librium).

Logarithmic plot of the counting rate of the eluted daughter substance as afunction of time.

2. To measure the activity of the iso-tope generator as a function oftime immediately after elution.

3. To measure the activity of a fresh-ly eluted solution of Ba-137 m asa function of time.

Isotope generator Cs-137/ Ba, 370 kBq 09047.60 1

Pulse rate meter 13622.93 1


Counter tube, type A, BNC 09025.11 1


Aluminium, sheet, 1 x 20 x 200 mm, 5 pcs. 31074.00 1






Test tube, AR-glass, d = 16 mm 37656.10 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedHalf-line and radioactive equilibrium P2520101

Physical Structure of Matter Radioactivity


� Parent substance� Daughter substance� Rate of decay� Disintegration or decay

constant� Counting rate� Half life� Disintegration product

LEP_5_1 09.08.2007 12:13 Uhr Seite 216


Half-life and radioactive equilibrium with Cobra3 5.2.01-11

Radioactivity Physical Structure of Matter

Principle:The half-life of a Ba-137 m daughtersubstance eluted (washed) out of aCa-137 isotope generator is meas-ured directly and is also determinedfrom the increase in activity afterelution.

Logarithmic plot of the counting rate of Ba-137m’s decay; counting rate as afunction of time, with the regression line.

Tasks:1. To record the counting rate as a

function of the counter tube volt-age (counter tube characteristic)when the isotope generator activ-ity is constant (radioactive equi-librium).

2. To measure the activity of the iso-tope generator as a function oftime immediately after elution.

3. To measure the activity of a fresh-ly eluted solution of Ba-137 m asa function of time.


� Parent substance� Daughter substance� Rate of decay� Disintegration or decay

constant� Counting rate� Half life� Disintegration product



Software Cobra3 Radioactivity 14506.61 1

Cobra3 measuring Module GM counting tube 12106.00 1

Base plate for radioactivity 09200.00 1

Counter tube holder on fixing magnet 09201.00 1

Plate holder on fixing magnet 09203.00 1

Source holder on fixing magnet 09202.00 1



Test tube, FIOLAX®, d = 12 mm 36307.10 1

Rubber stopper, d = 14.5/10.5 mm, without hole 39253.00 1

Isotope generator Cs-137/ Ba, 370 kBq 09047.60 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedHalf-life and radioactive equilibriumwith Cobra3 P2520111

LEP_5_1 09.08.2007 12:13 Uhr Seite 217

5.2.03-11 Poisson’s distribution and Gaussian distribution of radioactive decay with Cobra3– Influence of the dead time of the counter tube

Principle:1) The aim of this experiment is toshow that the number of pulsescounted during identical time inter-vals by a counter tube which bears afixed distance to a long-lived radia-tion emitter correspond to a Pois-son’s distribution. A special charac-teristic of the Poisson’s distributioncan be observed in the case of asmall number of counts n <20: Thedistribution is unsymmetrical, i. e.the maximum can be found among

smaller numbers of pulses than themean value. In order to show thisunsymmetry the experiment is car-ried out with a short counting periodand a sufficiently large gap betweenthe emitter and the counter tube sothat the average number of pulsescounted becomes sufficiently small.

2) Not only the Poisson’s distribution,but also the Guassian distributionwhich is always symmetrical is verysuitable to approximate the pulsedistribution measured by means of along-lived radiation emitter and a

Pulse rate distribution for high pulse rate (248 pulses/s) with an adaptedGaussian curve (left window) and a Poisson’s curve (right window).

counter tube arranged with a con-stant gap between each other. Apremise for this is a sufficiently highnumber of pulses and a large sam-pling size.

The purpose of the following experi-ment is to confirm these facts and toshow that the statistical pulse distri-bution can even be be approximatedby a Guassian distribution, when(due to the dead time of the countertube) counting errors occur leadingto a distribution which deviates fromthe Poisson’s distribution.


� Poisson’s distribution� Gaussian distribution� Standard deviation� Expected value of pulse rate� Different symmetries of

distributions� Dead time� Recovering time and

resolution time of a countertube






Cobra3 measuring Module GM counting tube 12106.00 1





Americium-241 source, 370 kBq 09090.11 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedPoisson’s distribution and Gaussian distribution of radioactive decay with Cobra3 – Influence of the dead time of the counter tube P2520311



3) If the dead time of the countertube is no longer small with regardto the average time interval betweenthe counter tube pulses, the fluctua-tion of the pulses is smaller than inthe case of a Poisson’s distribution.In order to demonstrate these factsthe limiting value of the mean value(expected value) is compared to thelimiting value of the variance bymeans of a sufficiently large sam-pling size.

LEP_5_1 09.08.2007 12:13 Uhr Seite 218



Visualisation of radioactive particles / Diffusion cloud chamber 5.2.04-00

Principle:Radioactivity is a subject in our soci-ety which has been playing animportant role throughout politics,economy and media for many yearsnow. The fact that this radiation can-not be seen or felt by the humanbeing and that the effects of thisradiation are still not fully exploredyet, causes emotions like no otherscientific subject before.

The high-performance diffusioncloud chamber serves for making the

tracks of cosmic and terrestrial radi-ation visible so that a wide range ofnatural radiation types can be iden-tified. Furthermore, the diffusioncloud chamber offers the opportu-nity to carry out physical experi-ments with the aid of artificial radi-ation sources.

Experimental set-up: deflection of �-particles.

Tasks:1. Determination of the amount of

background radiation

2. Visualisation of �, �, �-particlesand mesons

3. Visualisation of the Thorium(Radon) decay

4. Deflection of �--particles in amagnetic field

Diffusion cloud chamber PJ45, 230 V 09046.93 1

Isopropyl alcohol, 1000 ml 30092.70 2

Thorium-source 09043.41 1

Radioactive source, Sr-90, 74kBq 09047.53 1






Holder for dynamometer 03068.04 1

Scale for demonstration board 02153.00 1

Accessory set for Beta deflection 09043.52 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedVisualisation of radioactive particles /Diffusion cloud chamber P2520400


� �, �, �-particles� � deflection� Ionising particles� Mesons� Cosmic radiation� Radioactive decay� Decay series� Particle velocity� Lorentz force

LEP_5_1 09.08.2007 12:13 Uhr Seite 219


5.2.20-15 Alpha-Energies of different sources with Multi Channel Analyzer

Principle:An Alpha-spectrometer, consisting ofa photodetector, a preamplifier, apulse height analyser and a record-ing device for registration of thespectra is calibrated by means of anopen Alpha-emitter of known Alpha-energy (241Am). The energy spectrumof a radium source which is in equi-librium with its decay products, isrecorded and evaluated. The Alpha-Energies found in this way are allo-cated to the corresponding nuclidesof the radium decay series.

Alpha-spectrum of the 226Ra.

Tasks:1. The Alpha-spectrum of the 226Ra

is recorded with Multi ChannalAnalyzer

2. The calibration spectrum of theopen 241Am Alpha-emitter isrecorded at the same settings.

3. The Alpha-energies correspondingto the individual peaks of theAlpha-spectrum of the radium arecalculated and compared to thevalues in the literature.

Multi-Channel-Analyzer 13726.99 1

Software Multi-Channel-Analyzer 14452.61 1

Americium-241 source, 3.7 kBq 09090.03 1

Radioactive Source Ra-226, 4 kBq 09041.00 1

Alpha- and Photodetector 09099.00 1

Pre-amplifier for alpha detector 09100.10 1




Cable connector BNC, 75 Ω 07542.09 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedAlpha-Energies of different sources with Multi Channel Analyzer P2522015


� Decay series� Radioactive equilibrium� Isotopic properties� Decay energy� Particle energy� Potential well model of the

atomic nucleus� Tunnel effect� Geiger-Nuttal law� Semiconductor� Barrier layer


LEP_5_1 09.08.2007 12:13 Uhr Seite 220


Rutherford experiment 5.2.21-01/11/15


Principle:The relationship between the angleof scattering and the rate of scatter-ing of �-particles by gold foil isexamined with a semiconductordetector. This detector has a detec-tion probability of 1 for �-particlesand virtually no zero effect, so thatthe number of pulses agrees exactlywith the number of �-particles strik-ing the detector.

In order to obtain maximum possiblecounting rates, a measurementgeometry is used which dates back

to Chadwick. It is also possible in thiscase to shift the foil and source in anaxial direction (thus deviating fromChadwick’s original apparatus), sothat the angle of scattering can bevaried over a wide range.

In addition to the annular diaphragmwith gold foil, a second diaphragmwith aluminium foil is provided inorder to study the influence of thescattering material on the scatteringrate.

Counting rate for gold as a function of .1(r2)2sin4(�

2)

Tasks:1. The particle rates are measured at

different angles of scatteringbetween about 20 ° and 90 °. Themeasurements are compared withthe particle rates calculated bymeans of the Rutherford theoryfor the measurement geometryused.

2. The particle rates are measured inthe case of scattering by alumin-ium and gold with identical anglesof scattering in each case. Theratio of the two particle rates iscompared with the particle ratecalculated from Rutherford’s scat-tering equation.


� Scattering� Angle of scattering� Impact parameter� Central force� Coulomb field� Coulomb forces� Rutherford atomic model� Identity of atomic number

and charge on the nucleus

Experiment P2522115 with MCAExperiment P2522111 with Cobra3Experiment P2522101 with digital counterMulti-Channel-Analyzer 13726.99 1Software Multi-Channel-Analyzer 14452.61 1Alpha- and Photodetector* 09099.00 1 1 1Annular diaphragm with gold foil 09103.02 1 1 1Annular diaphragm with aluminium foil 09103.03 1 1 1U-magnet, large 06320.00 1 1 1Americium-241 source, 370 kBq 09090.11 1 1 1Container for nuclear physics experiments 09103.00 1 1 1Pre-amplifier for alpha detector 09100.10 1 1 1Pulse height analyser 13725.93 1 1Digital counter, 4 decades 13600.93 1Hand held measuring instrument Pressure, RS 232 07136.00 1 1Pressure sensor, 1.0...1300 hPa 07136.01 1 1 1Diaphragm pump, two stage, 220V 08163.93 1 1 1Rubber tubing/vacuum, d = 6 mm 39286.00 3 3 3Tubing connect.,Y-shape, d = 8-9 mm 47518.03 1 1 1Oscilloscope 30 MHz, 2 channels 11459.95 1Pinchcock, width 20 mm 43631.20 1 1 1Screened cable, BNC, l = 750 mm 07542.11 4 4 3Adapter BNC socket/4 mm plug pair 07542.27 1 1Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 2 2Data cable 2 x SUB-D, plug/socket, 9 pole 14602.00 1Cobra3 BASIC-UNIT, USB 12150.50 1Software Cobra3 Radioactivity 14506.61 1Power supply 12V/2A 12151.99 1PC, Windows® 95 or higher

* Alternatively:Alpha detector 09100.00 1 1 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedRutherford experiment P2522101/11/15

Set-up of experiment P2522115 with MCA

LEP_5_1 09.08.2007 12:13 Uhr Seite 221

Principle:The �-spectrum of an open 241Am-emitter is measured with a semi-conductor �-detector, maximum usebeing made in this case of the reso-lution capacity of the pulse heightanalyzer. Use is made for this pur-pose of the “Zoom” function, whichis an additional amplification stagehaving in the effect that only thatproportion of the pulses exceedingthe threshold voltage of 5 V under-goes further processing. The pulsepeaks above this threshold areamplified 5 times and restricted to amaximum of 10 V.

Tasks:1. The spectrum of an open 241Am-

emitter is recorded with the xyt-recorder at the maximum resolu-tion capacity of the measurementlayout, using automatic windowmovement. The energy of the twopeaks preceding the principal peakis calculated. The principal peak,corresponding to a particle energyof 5.486 MeV, is used for calibra-tion purposes.

Measured Alpha-spectrum of Am-241.

2. The resolution capacity of themeasurement layout is measuredfrom the half-life width of theprincipal peak.


� Energy level diagram (decaydiagram)

� Transition probability� Excited nuclear states� �-emission� Connection between the fine

structure of the �-spectrumand the accompanying �-spectrum

Experiment P2522215 with MCAExperiment P2522211 with Cobra3Experiment P2522201 with xyt recorder

Multi-Channel-Analyzer 13726.99 1Software Multi-Channel-Analyzer 14452.61 1Alpha- and Photodetector* 09099.00 1 1Americium-241 source, 3.7 kBq 09090.03 1 1 1Container for nuclear physics experiments 09103.00 1 1 1Pre-amplifier for alpha detector 09100.10 1 1 1Pulse height analyser 13725.93 1 1XYt recorder 11416.97 1Hand held measuring instrument Pressure, RS 232 07136.00 1 1 1Pressure sensor, 1.0...1300 hPa 07136.01 1 1 1Diaphragm pump, two stage, 220V 08163.93 1 1 1Rubber tubing/vacuum, d = 6 mm 39286.00 3 3 3Tubing connect.,Y-shape, d = 8-9 mm 47518.03 1 1 1Oscilloscope 30 MHz, 2 channels 11459.95 1 1Pinchcock, width 20 mm 43631.20 1 1 1Screened cable, BNC, l = 750 mm 07542.11 4 4 3Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 2 2Data cable 2 x SUB-D, plug/socket, 9 pole 14602.00 1Cobra3 BASIC-UNIT, USB 12150.50 1Software Cobra3 Universal recorder 14504.61 1Power supply 12V/2A 12151.99 1PC, Windows® 95 or higher

* Alternatively:Alpha detector 09100.00 1 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFine structure of the �-spectrum of 241Am P25222 01/11/15





LEP_5_1 09.08.2007 12:13 Uhr Seite 222



Study of the �-energies of 226Ra 5.2.23-01/11/15

Principle:An �-spectrometer, consisting of asilicon surface barrier layer detector,a preamplifier, a pulse height analyz-er and a recording device for regis-tration of the spectra is calibrated bymeans of an open �-emitter ofknown �-energy (241Am).

The energy spectrum of a radiumsource which is in equilibrium withits decay products, is recorded and

evaluated. The �-energies found inthis way are allocated to the corre-sponding nuclides of the radiumdecay series.

Tasks:1. The �-spectrum of the 226Ra is

recorded, the settings of the pulseanalyzer (amplification) andrecorder (x and y input sensitivity)being selected so as to make bestpossible use of the recordingwidth.

2. The calibration spectrum of theopen 241Am-emitter is recorded atthe same settings.

226Ra pulse rate dependence of pulse height.

3. The �-energies corresponding tothe individual peaks of the �-spectrum of the radium are calcu-lated and, on the assumption of aconstant energy loss in the sourcecovering, the �-active nuclides ofthe radium decay series corre-sponding to the individual peaksare determined on the basis of thevalues in the literature.


� Decay series� Radioactive equilibrium� Isotopic properties� Decay energy� Particle energy� Potential well model of the

atomic nucleus� Tunnel effect� Geiger-Nuttal law� Semiconductor� Barrier layer


Multi-Channel-Analyzer 13726.99 1Software Multi-Channel-Analyzer 14452.61 1Alpha- and Photodetector* 09099.00 1 1 1Americium-241 source, 3.7 kBq 09090.03 1 1 1Adaptor for radioactive sources 09043.29 1 1 1Radioactive Source Ra-226, 4 kBq 09041.00 1 1 1Container for nuclear physics experiments 09103.00 1 1 1Pre-amplifier for alpha detector 09100.10 1 1 1Pulse height analyser 13725.93 1 1XYt recorder 11416.97 1Hand held measuring instrument Pressure, RS 232 07136.00 1 1 1Pressure sensor, 1.0...1300 hPa 07136.01 1 1 1Diaphragm pump, two stage, 220V 08163.93 1 1 1Rubber tubing/vacuum, d = 6 mm 39286.00 3 3 3Tubing connect.,Y-shape, d = 8-9 mm 47518.03 1 1 1Oscilloscope 30 MHz, 2 channels 11459.95 1 1Pinchcock, width 20 mm 43631.20 1 1 1Screened cable, BNC, l = 750 mm 07542.11 4 4 4Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 2 2Data cable 2 x SUB-D, plug/socket, 9 pole 14602.00 1Cobra3 BASIC-UNIT, USB 12150.50 1Software Cobra3 Universal recorder 14504.61 1Power supply 12V/2A 12151.99 1PC, Windows® 95 or higher

* Alternatively:Alpha detector 09100.00 1 1 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedStudy of the �-energies of 226Ra P25223 01/11/15


LEP_5_1 09.08.2007 12:13 Uhr Seite 223

Principle:A study is made of the connectionbetween the energy E of �-particlesand the path x travelled by them inair at standard pressure. The meas-urements recorded enable the diffe-rencial energy loss dE/dx to be cal-culated as a function of x.

Tasks:1. The spectrum of a covered 241Am

source is measured at a fixed dis-tance s as a function of the pres-sure p. The distance s is selectedin such a way as to correspond tothe maximum range at the highestpressure measurable with themanometer used. The energy cor-responding to the central points ofthe individual spectra are deter-mined (after calibration of themeasurement layout with an open241Am-emitter, see 3.) and plottedas a function of the distance xconverted to a 1013 hPa basis.Using this function, the differen-tial energy loss (–dE/dx) is thencalculated as a function of x andagain plotted on the graph.

2. The spectrum of the source usedin 1. is measured initially underthe same geometric conditionsunder vacuum and subsequentlywith the vessel filled with helium,nitrogen or carbon dioxide, ineach case under identical pres-sures. The different energy lossvalues are compared with theelectron concentration in the par-ticluar gas.

3. The mean energy with which the�-particles leave the coveredamericium source is determinedby calibration against the openamericium emitter (E = 5.485MeV). (This value is required forthe evaluation in 1.)


� Range� Range dispersion� Mean free path length� Mean ionization energy of

gas atoms� Mean energy loss of

�-particles per collision� Differencial energy loss� Bethe formula� Electron concentration in

gases

Experiment P2522415 with MCAExperiment P2522411 with Cobra3Experiment P2522401 with xyt recorderMulti-Channel-Analyzer 13726.99 1Software Multi-Channel-Analyzer 14452.61 1Alpha- and Photodetector* 09099.00 1 1 1Americium-241 source, 3.7 kBq 09090.03 1 1 1Americium-241 source, 370 kBq 09090.11 1 1 1Container for nuclear physics experiments 09103.00 1 1 1Pre-amplifier for alpha detector 09100.10 1 1 1Pulse height analyser 13725.93 1 1XYt recorder 11416.97 1Hand held measuring instrument Pressure, RS 232 07136.00 1 1 1Pressure sensor, 1.0...1300 hPa 07136.01 1 1 1Diaphragm pump, two stage, 220V 08163.93 1 1 1Rubber tubing/vacuum, d = 6 mm 39286.00 3 3 3Tubing connect.,Y-shape, d = 8-9 mm 47518.03 1 1 1Oscilloscope 30 MHz, 2 channels 11459.95 1 1Pinchcock, width 20 mm 43631.20 1 1 1Glass stopcocks, 3 way, T-shaped 36731.00 1 1 1Fine control valve for pressure bottles 33499.00 1 1 1Compressed gas, helium, 12 l 41772.03 1 1 1Compressed gas, nitrogen, 12 l 41772.04 1 1 1Compressed gas, CO2, 21 g 41772.06 1 1 1Screened cable, BNC, l = 750 mm 07542.11 4 4 3Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 2 2Data cable 2 x SUB-D, plug/socket, 9 pole 14602.00 1Cobra3 BASIC-UNIT, USB 12150.50 1Software Cobra3 Universal recorder 14504.61 1Power supply 12V/2A 12151.99 1

* Alternatively:Alpha detector 09100.00 1 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedEnergy loss of �-particles in gases P25224 01/11/15




Influence of the type of gas on the energy loss of �-particles.

Set-up of experiment P2522401 with xyt recorder

LEP_5_1 09.08.2007 12:13 Uhr Seite 224



Electron absorption 5.2.31-00

Principle:The attenuation of an electron parti-cle stream passing through a materi-al layer depends both on the thick-ness of the layer and on the masscoverage, resp. the “mass per unitarea”. It will be shown that the parti-cle flux consisting of electrons of aparticular energy distribution de-creases with the “mass per unit area”.As electron source, a radioactivesample of Sr90 is used.

Tasks:1. The �-counting rates are meas-

ured as a function of the absorberthickness using different absorb-ing materials such as aluminium(AL), glass (GL), hard paper (HP),and typing paper (TP).

Counting rate �I as a function of absorber thickness.

2. The attenuation coefficients areevaluated for the four absorbingmaterials and plotted as a func-tion of the density.


Geiger-Müller Counter 13606.99 1





Supports for base 09200.00, 2 pcs. 09200.01 1





Absorption plates for beta-rays 09024.00 1

Cover glasses, 40 x 22 mm, 50 pcs. 64688.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedElectron absorption P2523100


� Density� Counter tube� Radioactive decay� Attenuation coefficient� Mass coverage

LEP_5_1 09.08.2007 12:13 Uhr Seite 225


Principle:The radiation of �-unstable atomicnuclei is selected on the basis of itspulses in a magnetic transverse field,using a diaphragm system. The rela-tionship between coil current andparticle energy is determined for cal-ibration of the spectrometer and thedecay energy of the �-transition isobtained in each case from the �–-spectra.

�-spectrum of 90Sr.

Tasks:1. Energy calibration of the magnet-

ic spectrometer.

2. Measurement of the �-spectra of90Sr and 22Na.

3. Determination of the decay energyof the two isotopes.


� �–-decay� �+-decay� Electron capture� Neutrino� Positron� Decay diagram� Decay energy� Resting energy� Relativistic Lorentz equation

Beta-spectroscope 09104.00 1

Iron core, solid, 25 mm long 06490.01 1




Coil, 600 turns 06514.01 1

Radioactive source, Na-22, 74kBq 09047.52 1



Geiger-Müller Counter 13606.99 1








What you need:

Complete Equipment Set, Manual on CD-ROM included�-spectroscopy P2523200



LEP_5_1 09.08.2007 12:13 Uhr Seite 226



Law of distance and absorption of gamma or beta rays 5.2.41-01/11

Principle:The inverse square law of distance isdemonstrated with the gamma radi-ation from a 60Co preparation, thehalf-value thickness and absorption

coefficient of various materialsdetermined with the narrow beamsystem and the corresponding massattenuation coefficient calculated.

Tasks:1. To measure the impulse counting

rate as a function of the distancebetween the source and the coun-ter tube.

2. To determine the half-value thick-ness d1/2 and the absorption coef-ficient of a number of materialsby measuring the impulse count-

Attenuation coefficient of different materials as a function of the materi-al density (from left to right: Plexiglas®, concrete, aluminium, iron, lead).

ing rate as a function of the thick-ness of the irradiated material.Lead, iron, aluminium, concreteand Plexiglas are used as absorb-ers.

3. To calculate the mass attenuationcoefficient from the measuredvalues.


� Radioactive radiation� Beta-decay� Conservation of parity� Antineutrino� Gamma quanta� Half-value thickness� Absorption coefficient� Term diagram� Pair formation� Compton effect� Photoelectric effect� Conservation of angular

momentum� Forbidden transition� Weak interaction� Dead time

Experiment P2524111 with Cobra3Experiment P2524101 with GM Counter

Radioactive sources, set 09047.50 1 1

Absorption plates for beta-rays 09024.00 1 1

Base plate for radioactivity 09200.00 1 1

Counter tube holder on fixing magnet 09201.00 1 1

Source holder on fixing magnet 09202.00 1 1

Plate holder on fixing magnet 09204.00 1 1

Counter tube, type A, BNC 09025.11 1 1

Screened cable, BNC, l = 300 mm 07542.10 1 1

Vernier caliper, plastic 03011.00 1 1

Geiger-Mueller-Counter 13606.99 1

Absorption material, lead 09029.01 1 1

Absorption material, iron 09029.02 1 1

Absorption material, aluminium 09029.03 1 1

Absorption material, Plexiglas 09029.04 1 1

Absorption material, concrete 09029.05 1 1




Counter tube module 12106.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedLaw of distance and absorption of gammaor beta rays P2524101/11

µcm

g cm


LEP_5_1 09.08.2007 12:13 Uhr Seite 227

Principle:The intensity of �-radiation decreas-es when it passes through solid mat-ter. The attenuation can be the resultof Compton scattering, the photoeffect or the pair production. Anabsorption coefficient can be attrib-uted to each of the three phenome-na. These absorption coefficients, aswell as the total absorption, arehighly energy-dependent. The energydependence of the total absorptioncoefficient for aluminium in therange below 1.3 MeV is verified.

Total gamma-absorption coefficient as a function of the energy.

Tasks:1. For each of the emitting isotopes

Na22, Cs137 and Am241 the �-spec-trum is traced and a tresholdenergy, Ethres, just below thephoto-peak in the high energyrange determined.

2. Using the scintillation counter inconjunction with the pulse heightanalyser as a monochromator, the�-intensity is measured as a func-tion of the thickness of differentaluminium layers. The three �-emitting isotopes are used succes-sively as the source, assuming thatthe energy of the emitted �-radi-ation is known.


� Compton scattering� Photo effect� Pair production� Absorption coefficient� Radioactive decay� �-spectroscopy


Multi-Channel-Analyzer 13726.99 1Software for Multi-Channel-Analyzer 14452.61 1Americium-241 source, 370 kBq 09090.11 1 1 1Radioactive Source Cs-137, 37kBq 09096.01 1 1 1Gamma detector 09101.00 1 1 1Operating unit for gamma detector 09101.93 1 1 1High voltage connecting cable 09101.10 1 1 1Pulse height analyser 13725.93 1 1Oscilloscope 30 MHz, 2 channels 11459.95 1xyt recorder 11416.97 1Base plate for radioactivity 09200.00 1 1 1Plate holder on fixing magnet 09203.00 1 1 1Lab jack, 160 x 130 mm 02074.00 1 1 1Vernier calipers, stainless steel 03010.00 1 1 1Source holder on fixing magnet 09202.00 1 1 1Absorption material, aluminium 09029.03 1 1 1Adapter BNC socket/4 mm plug pair 07542.27 2 1Screened cable, BNC, l = 750 mm 07542.11 4 2 1Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 2 2Data cable 2 x SUB-D, plug/socket, 9 pole 14602.00 1Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 1Software Cobra3 Universal recorder 14504.61 1Software Cobra3 Radioactivity 14506.61 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedEnergy Dependence of the �-absorptionCoefficient 25242 01/11/15


5.2.42-01/11/15 Energy Dependence of the �-absorption Coefficient



LEP_5_1 09.08.2007 12:13 Uhr Seite 228



Compton effect 5.2.44-01/11/15

Principle:The energy of scattered �-radiationis measured as a function of theangle of scatter. The Compton wave-length is determined from the mea-sured values.

Energy of known peaks as a function of the pulse height.

Tasks:1. Calibrate the measuring set-up

with the aid of a Cs-137 calibrat-ing source (37 kBq), an Am-241source (370 kBq) and a Na-22source (74 kBq).

2. Measure the energy of the Cs-137661.6 keV peaks scattered at dif-ferent angles and calculate theCompton wavelength from thereadings taken.


� Corpuscle� Scattering� Compton wavelength� �-quanta� De Broglie wavelength� Klein-Nishina formula



Software for Multi-Channel-Analyzer 14452.61 1

Radioactive source, Na-22, 74kBq 09047.52 1 1 1

Americium-241 source, 370 kBq 09090.11 1 1 1

Radioactive Source Cs-137, 37kBq 09096.01 1 1 1

Radioactive source Cs-137,18.5 MBq 09096.20 1 1 1

Gamma detector 09101.00 1 1 1

Operating unit for gamma detector 09101.93 1 1 1

High voltage connecting cable 09101.10 1 1 1

Pulse height analyser 13725.93 1 1

Oscilloscope 30 MHz, 2 channels 11459.95 1 1

xyt recorder 11416.97 1

Shielding cylinder for gamma-detector 09101.11 1 1 1

Rod, iron, d = 25 mm, l = 200 mm 09101.13 1 1 1

Lead block, 200 x 100 x 50 mm 09029.11 1 1 1

Lead brick with hole 09021.00 1 1 1

Source holder on fixing magnet 09202.00 1 1 1

Adapter BNC socket/4 mm plug pair 07542.27 1 1

Screened cable, BNC, l = 750 mm 07542.11 3 3 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedCompton effect P25244 01/11/15


LEP_5_1 09.08.2007 12:13 Uhr Seite 229




Principle:The radiation emitted during thedecay of the 137Cs isotope is mea-sured with a scintillation detectorand the energy spectrum determinedwith a pulse height analyzer. Thespectrum contains fractions due to a

�-transition and fractions originat-ing from a characteristic X-ray radi-ation. The areas of the fractions inquestion are determined and theconversion factor obtained fromthem.

�-spectrum of 137Cs. F_x corresponds to characteristic X-ray radiation causedby internal conversion in Ba-137. F_y1 and F_y2 corresponds to the transi-tion radiation.

Tasks:1. Measurement of the g-spectrum

of 137Cs using a scintillation de-tector.

2. Determination of the conversionfactor of the 137mBa excited nu-cleus.


� �-radiation� Nuclear transitions� Transition probability� Duration� Metastable states� Isotopic spin quantum

numbers� Rules governing selection� Multipole radiation� Isomeric nuclei� Photonuclear reaction� Conversion electron� Characteristic X-ray radiation� Scintillation detectors









Oscilloscope 30 MHz, 2 channels 11459.95 1 1

XYt recorder 11416.97 1

Support rod -PASS-, square, l = 400 mm 02026.55 1 1 1

Right angle clamp -PASS- 02040.55 1 1 1

Tripod base -PASS- 02002.55 1 1 1

Adapter BNC socket/4 mm plug pair 07542.27 1 1









What you need:

PComplete Equipment Set, Manual on CD-ROM includedInternal conversion in 137mBa P25245 01/11/15

Set-up of experiment P2524501 with xyt recorder

LEP_5_1 09.08.2007 12:13 Uhr Seite 230


Radioactivity Physical structure of matter

Photonuclear cross-section / Compton scattering cross-section 5.2.46-01/11/15

Principle:The radiation of 137Cs and 22Na ismeasured with a scintillation detec-tor and the energy spectrum deter-mined with a pulse height analyzer.The fractions of the spectra causedby Compton scattering and thosecaused by the photoelectric effectare determined on the basis of theirareas. The results are used for deter-mining the ratio of the effectivecross-sections and examining itsenergy dependence.

�-spectrum of 22Na.

Tasks:1. Measurement of the g-spectra of

22Na and 137Cs, using a scintilla-tion detector.

2. Determination of the ratio of thespecific effective cross-sectionsdue to the Compton effect and thephotoelectric effect in photonshaving energy values of 511, 662and 1275 keV.


� �-radiation� Interaction with material� Photoelectric effect� Compton effect� Pair formation� Detection probability� Scintillation detectors




Radioactive source, Na-22, 74kBq 09047.52 1 1 1








Support rod -PASS-, square, l = 400 mm 02026.55 1 1 1

Universal clamp 37718.00 1 1 1

Right angle clamp -PASS- 02040.55 2 2 2

Tripod base -PASS- 02002.55 1 1 1










What you need:

Complete Equipment Set, Manual on CD-ROM includedPhotonuclear cross-section / Comptonscattering cross-section P25246 01/11/15


LEP_5_2 09.08.2007 12:18 Uhr Seite 231

Principle:The irradiation of strontinum (sul-phate), cadmium, indium, iodine andbarium (chloride) with soft �-radia-tions gives rise to Ka radiationscharacteristics of these elements.The X-ray spectra are recorded witha �-spectrometer consisting of ascintillation counter, a pulse heightanalyser and a recorder. After cali-bration of the spectrometer, the Ryd-berg constant is determined from theenergies of the X-ray lines, usingMoseley’s law.

Calibration lines of Cs-137 and Am-241

Tasks:1. Calibration of the �-spectrometer

in the low energy range, using theBa-resonance line of a 137Cs emit-ter (32 keV) and the �-line of241Am at 59.6 keV.

2. Recording of the X-ray fluores-cence spectra (Ka-lines) of differ-ent elements and determinationof the corresponding energies.

3. Plotting of the measured X-rayenergies according to Moseley’slaw against (Z-1)2 and determi-nation of the Rydberg constantR∞ from the slope of the resultinglines.


� Binding energy� Photoelectric eftect� Shell structure of electron

shells� Characteristic X-ray radiation� �-spectrometry� X-ray spectral analysis


Multi-Channel-Analyzer 13726.99 1Software Multi-Channel-Analyzer 14452.61 1Americium-241 source, 370 kBq 09090.11 1 1 1Radioactive Source Cs-137, 37kBq 09096.01 1 1 1Pulse height analyser 13725.93 1 1Gamma detector 09101.00 1 1 1Operating unit for gamma detector 09101.93 1 1 1High voltage connecting cable 09101.10 1 1 1Oscilloscope 30 MHz, 2 channels 11459.95 1XYt recorder 11416.97 1Adapter BNC socket/4 mm plug pair 07542.27 1Tin-II chloride 250 g 31991.25 1 1 1Silver foil sheet, 150 x 150 x 0.1 mm, 25 g 31839.04 1 1 1Absorption material, lead 09029.01 1 1 1Plastic bags, DIN A5, pack of 100 46444.01 1 1 1Crocodile clips, bare, 10 pcs 07274.03 1 1 1Support rod -PASS-, square, l = 250 mm 02025.55 3 3 3Support base -PASS- 02005.55 1 1 1Universal clamp 37718.00 1 1 1Right angle clamp -PASS- 02040.55 3 3 3Support rod with hole, stainless steel, l = 10 cm 02036.01 1 1 1Spring balance holder 03065.20 1 1 1Barium chloride, 250 g 30033.25 1 1 1Iodine resublimed, 25 g 30093.04 1 1 1Screened cable, BNC, l = 750 mm 07542.11 3 1 1Connecting cable, 4 mm plug, 32 A, red, l = 75 cm 07362.01 2 2Connecting cable, 4 mm plug, 32 A, blue, l = 75 cm 07362.04 2 2Data cable 2 x SUB-D, plug/socket, 9 pole 14602.00 1Cobra3 BASIC-UNIT, USB 12150.50 1Power supply 12V/2A 12151.99 1Software Cobra3 Universal recorder 14504.61 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray fluorescence and Moseley’s law P2524701/11/15



Physical structure of matter Radioactivity


LEP_5_2 09.08.2007 12:18 Uhr Seite 232


Solid-state Physics, Plasma Physics Physical Structure of Matter

Hall effect in p-germanium 5.3.01-01

Principle:The resistivity and Hall voltage of arectangular germanium sample aremeasured as a function of tempera-ture and magnetic field. The bandspacing, the specific conductivity,the type of charge carrier and themobility of the charge carriers aredetermined from the measurements.

2. The voltage across the sample ismeasured at room temperatureand constant control current as afunction of the magnetic induc-tion B.

3. The voltage across the sample ismeasured at constant controlcurrent as a function of the tem-

Hall voltage as a function of current.

Tasks:1. The Hall voltage is measured at

room temperature and constantmagnetic field as a function ofthe control current and plotted ona graph (measurement withoutcompensation for defect voltage).

Hall effect module 11801.00 1


Coil, 600 turns 06514.01 2


Pole pieces, plane, 30 x 30 x 48 mm, 1 pair 06489.00 1











What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in p-germanium P2530101


� Semiconductor� Band theory� Forbidden zone� Intrinsic conductivity� Extrinsic conductivity� Valence band� Conduction band� Lorentz force� Magnetic resistance� Mobility� Conductivity� Band spacing� Hall coefficient

Hall voltage as a function of magnetic induction.

perature. The band spacing of ger-manium is calculated from the mea-surements.

4. The Hall voltage UH is measuredas a function of the magnetic in-duction B, at room temperature.The sign of the charge carriersand the Hall constant RH togeth-

er with the Hall mobility mH and thecarrier concentration p are calculat-ed from the measurements.

5. The Hall voltage UH is measuredas a function of temperature atconstant magnetic induction Band the values are plotted on agraph.

LEP_5_2 09.08.2007 12:18 Uhr Seite 233


Physical Structure of Matter Solid-state Physics, Plasma Physics


Principle:The resistivity and Hall voltage of arectangular germanium sample aremeasured as a function of tempera-ture and magnetic field. The bandspacing, the specific conductivity,the type of charge carrier and themobility of the charge carriers aredetermined from the measurements.

4. The Hall voltage UH is measuredas a function of the magnetic in-duction B, at room temperature.The sign of the charge carriersand the Hall constant RH togeth-er with the Hall mobility mH andthe carrier concentration p arecalculated from the measure-ments.

5. The Hall voltage UH is measuredas a function of temperature atconstant magnetic induction Band the values are plotted on agraph.

Hall voltage as a function of temperature.

Tasks:1. The Hall voltage is measured at

room temperature and constantmagnetic field as a function ofthe control current and plotted ona graph (measurement withoutcompensation for defect voltage).

2. The voltage across the sample ismeasured at room temperatureand constant control current as afunction of the magnetic induc-tion B.

3. The voltage across the sample ismeasured at constant controlcurrent as a function of the tem-perature. The band spacing ofgermanium is calculated from themeasurements.


� Semiconductor� Band theory� Forbidden zone� Intrinsic conductivity� Extrinsic conductivity� Valence band� Conduction band� Lorentz force� Magnetic resistance� Mobility� Conductivity� Band spacing� Hall coefficient



Coil, 600 turns 06514.01 2














Software Cobra3 Hall effect 14521.61 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in p-germanium with Cobra3 P2530111

LEP_5_2 09.08.2007 12:18 Uhr Seite 234


Solid-state Physics, Plasma Physics Physical Structure of Matter

Hall effect in n-germanium 5.3.02-01/11

Principle:The resistance and Hall voltage aremeasured on a rectangular strip ofgermanium as a function of the tem-perature and of the magnetic field.From the results obtained the energygap, specific conductivity, type ofcharge carrier and the carrier mobil-ity are determined.

4. At room temperature measure theHall Voltage UH as a function ofthe magnetic flux density B. Fromthe readings taken, determine theHall coefficient RH and the sign ofthe charge carriers. Also calculatethe Hall mobility mH and the carri-er density n.

5. Measure the Hall voltage UH as afunction of temperature at uni-form magnetic flux density B, andplot the readings on a graph.

Tasks:1. At constant room temperature

and with a uniform magnetic fieldmeasure the Hall voltage as afunction of the control currentand plot the values on a graph(measurement without compensa-tion for error voltage).

2. At room temperature and with aconstant control current, measurethe voltage across the specimenas a function of the magnetic fluxdensity B.

3. Keeping the control current con-stant measure the voltage acrossthe specimen as a function oftemperature. From the readingstaken, calculate the energy gap ofgermanium.


� Semiconductor� Band theory� Forbidden zone� Intrinsic conduction� Extrinsic conduction� Valence band� Conduction band� Lorentz force� Magneto resistance� Neyer-Neldel Rule


Hall effect module 11801.00 1 1

Hall effect, n-Ge, carrier board 11802.01 1 1

Coil, 600 turns 06514.01 2 2

Iron core, U-shaped, laminated 06501.00 1 1

Pole pieces, plane, 30 x 30 x 48 mm, 1 pair 06489.00 1 1

Hall probe, tangential, with protective cap 13610.02 1 1

Power supply 0-12 V DC/ 6 V, 12 V AC 13505.93 1 1

Tripod base -PASS- 02002.55 1 1





Connecting cable, 4 mm plug, 32 A, black, l = 75 cm 07362.05 2 2









What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in n-germanium P25302 01/11

Hall voltage as a function of temperature.


LEP_5_2 09.08.2007 12:18 Uhr Seite 235



Principle:The Hall effect in thin zinc and cop-per foils is studied and the Hall coef-ficient determined. The effect oftemperature on the Hall voltage isinvestigated.

Hall voltage as a function of magnetic induction B, using a copper sample.

Tasks:1. The Hall voltage is measured in

thin copper and zinc foils.

2. The Hall coefficient is determinedfrom measurements of the currentand the magnetic induction.

3. The temperature dependence ofthe Hall voltage is investigated onthe copper sample.

Hall effect, Cu, carrier board 11803.00 1

Hall effect, Zn, carrier board 11804.01 1

Coil, 300 turns 06513.01 2



Power supply, stabilised, 0...30 V- / 20 A 13536.93 1






Meter 10/30 mV, 200°C 07019.00 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in metals P2530300

Physical structure of matter Solid-state Physics, Plasma Physics


� Normal Hall effect� Anomalous Hall effect� Charge carriers� Hall mobility� Electrons� Defect electrons

LEP_5_2 09.08.2007 12:18 Uhr Seite 236


Band gap of germanium 5.3.04-01

Solid-state Physics, Plasma Physics Physical structure of matter

Principle:The conductivity of a germaniumtestpiece is measured as a functionof temperature. The energy gap isdetermined from the measured val-ues.

Regression of the conductivity versus the reciprocal of the absolute temper-ature.

Tasks:1. The current and voltage are to be

measured across a germaniumtest-piece as a function of tem-perature.

2. From the measurements, the con-ductivity � is to be calculated andplotted against the reciprocal ofthe temperature T. A linear plot isobtained, from whose slope theenergy gap of germanium can bedetermined.


� Semiconductor� Band theory� Forbidden band� Intrinsic conduction� Extrinsic conduction� Impurity depletion� Valence band� Conduction band


Intrinsic conductor, Ge, carrier board 11807.01 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedBand gap of germanium P2530401

LEP_5_2 09.08.2007 12:18 Uhr Seite 237



Principle:The conductivity of a germaniumtestpiece is measured as a functionof temperature. The energy gap isdetermined from the measured val-ues.

Typical measurement of the probe-voltage as a function of the temperature.

Tasks:1. The current and voltage are to be

measured across a germaniumtest-piece as a function of tem-perature.

2. From the measurements, the con-ductivity � is to be calculated andplotted against the reciprocal ofthe temperature T. A linear plot isobtained, from whose slope theenergy gap of germanium can bedetermined.


Intrinsic conductor, Ge, carrier board 11807.01 1











What you need:

Complete Equipment Set, Manual on CD-ROM includedBand gap of germanium with Cobra3 P2530411



� Semiconductor� Band theory� Forbidden band� Intrinsic conduction� Extrinsic conduction� Impurity depletion� Valence band� Conduction band

LEP_5_2 09.08.2007 12:18 Uhr Seite 238


Surface treatment / Plasma Physics 5.3.10-00

Solid-state Physics, Plasma Physics Physical structure of matter

Principle:Different samples are exposed to adielectric barrier discharge in air atatmospheric pressure. The plasmainduces both chemical and physicalreactions on the sample surface al-tering the surface structure and thusthe surface energy. The contact angleof water on the sample surface isobserved in the exposed and in the

unexposed region to analyse theeffect of the plasma treatment onthe surface energy.

Measurement results for the contact angle of water on different samplesurfaces after plasma exposure of duration t.

Tasks:Various samples are to be treatedwith a plasma for different periods oftime. The effect of the treatment onthe contact angle of water on thesurface is to be observed by drop sizemeasurement or by web cam photo-graphy.


� Arc discharge� Glow discharge� Electron avalanches� Townsend breakthrough

mechanism� Streamers� Microdischarges� Dielectric barrier discharge

(DBD)� Surface energy� Contact angle (CA)� Contact angle measurement

Plasma Physics Operating Unit 09108.99 1

Plasma Physics Experimental Set 09108.10 1

Plasma Physics Sample Set 09108.30 1

Microliterpipette dig. 2-20 µl 47141.01 1

Pipette tips, 2-200 µl, 1000pcs 47148.01 1

Denatured alcohol (Spirit f.burning), 1000 ml 31150.70 1

Vernier caliper 03010.00 1

Water, distilled, 5 l 31246.81 1

Contact angle measurement equipment

Housing for experiment lamp 08129.01 1

Halogen lamp, 12 V/50 W 08129.06 1

Power supply 0-12V DC/6V,12V AC 13505.93 1

Lab jack, 160 x 130 mm 02074.00 1





Web-Cam CCD USB VGA PC Philips SPC900NC 88040.00 1

Software "Measure Dynamics", single user license 14440.62 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedSurface treatment / Plasma Physics P2531000

LEP_5_2 09.08.2007 12:18 Uhr Seite 239


5.3.11-00 Paschen curve / Plasma Physics

Principle:The electric breakthrough voltage inair is measured in dependence onelectrode distance and gas pressure.The results are compared to thePaschen curve which is a result ofTownsend electric breakdown theorywhich assumes the product pd ofelectrode distance d and gas pres-sure p to be the similarity parameterdescribing the electric breakdownbehavior of a gas.

Breakdown voltage in dependence on electrode distance for different gaspressures.

Tasks:Measure the voltage between planeparallel electrodes at which electricbreakthrough occurs in dependenceon electrode distance d at differentgas pressures p in the hPa range.

Create plots of the breakthroughvoltage over electrode distance dand over product of electrode dis-tance and pressure pd (Paschencurve).

Plasma Physics Operating Unit 09108.99 1

Plasma Physics Experimental Set 09108.10 1


Vacuum pump, one stage 02750.93 1

Oil mist filter 02752.00 1

Rubber tubing, vacuum, i.d. 8 mm 39288.00 2

Fine control valve 33499.00 1

Moving coil instrument 11100.00 1

Range multiplier, vacuum 11112.93 1

Tubing connect., T-shape, ID 8-9 mm 47519.03 1

Connecting cord, safety, 32 A, l = 100 cm, red 07337.01 1

Connecting cord, safety, 32A, l = 100 cm, blue 07337.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedPaschen curve / Plasma Physics P2531100



� Glow discharge� Electron avalanches� Free path length� Townsend breakdown theory� Paschen curve

LEP_5_2 09.08.2007 12:18 Uhr Seite 240


Characteristic X-rays of copper 5.4.01-00

X-ray Physics Physical structure of matter

Principle:Spectra of X-rays from a copperanode are to be analyzed by meansof different monocrystals and theresults plotted graphically. The ener-gies of the characteristic lines arethen to be determined from thepositions of the glancing angles forthe various orders of diffraction.

X-ray intensity of copper as a function of the glancing angle; LiF (100) mono-crystal as Bragg analyzer.


� Bremsstrahlung� Characteristic radiation� Energy levels� Crystal structures� Lattice constant� Absorption� Absorption edges� Interference� The Bragg equation� Order of diffraction

Tasks:1. The intensity of the X-rays emit-

ted by the copper anode at maxi-mum anode voltage and anodecurrent is to be recorded as afunction of the Bragg angle, usingan LiF monocrystal as analyzer.

2. Step 1 is to be repeated using theKBr monocrystal as analyzer.

3. The energy values of the charac-teristic copper lines are to be cal-culated and compared with theenergy differences of the copperenergy terms.

X-ray basic unit, 35 kV 09058.99 1

Goniometer for X-ray Unit 35 kV 09058.10 1

Plug-in module with Cu-X-ray tube 09058.50 1

Counter tube type B, BNC cable, l = 50 cm 09005.00 1

Lithium fluorid crystal, mounted 09056.05 1

Potassium bromide crystal, mounted 09056.01 1

Recording equipment:


Connecting cable, l = 100 cm, red 07363.01 2

Connecting cable, l = 100 cm, blue 07363.04 2

or

Software X-ray unit, 35 kV 14407.61 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristic X-rays of copper P2540100

LEP_5_2 09.08.2007 12:18 Uhr Seite 241


5.4.02-00 Characteristic X-rays of molybdenum

Principle:Spectra of X-rays from a molybde-num anode are to be analyzed bymeans of different monocrystals andthe results plotted graphically. Theenergies of the characteristic linesare then to be determined from thepositions of the glancing angles forthe various orders of diffraction.

X-ray intensity of molybdenum as a function of the glancing angle; LiF (100)monocrystal as Bragg analyzer.



Plug-in module with Mo-X-ray tube 09058.60 1








or

Software x-ray unit, 35 kV 14407.61 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristik X-rays of molybdenum P2540200

Physical structure of matter X-ray Physics


� X-ray tube� Bremsstrahlung� Characteristic radiation� Energy levels� Crystal structures� Lattice constant� Absorption� Absorption edges� Interference� The Bragg equation� Order of diffraction


ted by the molybdenum anode atmaximum anode voltage andanode current is to be recorded asa function of the Bragg angle,using an LiF monocrystal as ana-lyzer.


3. The energy values of the charac-teristic molybdenum lines are tobe calculated and compared withthe energy differences of themolybdenum energy terms.

LEP_5_2 09.08.2007 12:18 Uhr Seite 242


Characteristic X-rays of iron 5.4.03-00


Principle:Spectra of X-rays from a iron anodeare to be analyzed by means of dif-ferent monocrystals and the resultsplotted graphically. The energies ofthe characteristic lines are then to bedetermined from the positions of theglancing angles for the various or-ders of diffraction.

X-ray intensity of iron as a function of the glancing angle; LiF (100)monocrystal as Bragg analyzer.


� X-ray tube� Bremsstrahlung� Characteristic radiation� Energy levels� Crystal structures� Lattice constant� Absorption� Absorption edges� Interference� The Bragg equation� Order of diffraction


ted by the iron anode at maximumanode voltage and anode currentis to be recorded as a function ofthe Bragg angle, using an LiFmonocrystal as analyzer.


3. The energy values of the charac-teristic iron lines are to be calcu-lated and compared with the en-ergy differences of the iron energyterms.



Plug-in module with Fe-X-ray tube 09058.70 1








or




What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristik X-rays of iron P2540300

LEP_5_2 09.08.2007 12:18 Uhr Seite 243


5.4.04-00 The intensity of characteristic X-rays as a function of anode current and anode voltage

100 120 14020 40 60 80

7000

8000

9000

10000

1000

2000

3000

4000

5000

6000

Principle:Polychromatic X-radiation from acopper anode is to be directedagainst an LiF monocrystal so thatthe wavelengths can be analyzed ac-cording to Bragg. The dependency ofthe characteristic Ka and Kb radia-tion on the anode current and anodevoltage are to be determined.

Ka and Kb intensities as a function of (UA - UK)1.5 (IA = const.).

Tasks:1. The intensity spectrum of poly-

chromatic radiation from an X-raytube is to be recorded with thehelp of an LiF monocrystal.

2. The intensities of the characteris-tic Ka and Kb radiations are to bedetermined as a function of boththe anode current and the anodevoltage, and be plotted graphical-ly.

3. The results of the measurementare to be compared with the the-oretical intensity formula.










or




What you need:

Complete Equipment Set, Manual on CD-ROM includedThe intensity of characteristic X-rays as a function ofanode current and anode voltage P2540400



� Characteristic X-ray radiation� Energy levels� The Bragg equation� Intensity of characteristic

X-rays

(UA - UK)3/2/kV3/2

Kb

Ka

N

Imp s-1

LEP_5_2 09.08.2007 12:18 Uhr Seite 244


Monochromatization of molybdenum X-rays 5.4.05-00


Principle:Polychromatic X-rays are to be ener-gy analyzed using various monocrys-tals and a suitably selected thinmetal foil having an absorption edgewhich drastically reduces the inten-sity of an unwanted line.

3. The LiF monocrystal is to be usedto filter out a characteristic lineand the appertaining monochrom-atization graphically recorded.

4. Step 1 is to be repeated, using azirconium filter.

Molybdenum X-ray monochromatization with Zr filter; LiF (100) monocrystalas analyzer.


� Bremsstrahlung� Characteristic radiation� Energy levels� Absorption� Absorption edges� Interference� Diffraction� Bragg scattering


ted by the molybdenum anode isto be graphically recorded as afunction of the Bragg angle, usingLiF and KBr monocrystals succes-sively as analyzers.

2. The energy values of the charac-teristic molybdenum lines are tobe calculated.







Diaphragm tube with Zr- foil 09058.03 1





or




What you need:

Complete Equipment Set, Manual on CD-ROM includedMonochromatization of molybdenum X-rays P2540500

Molybdenum X-ray intensity as a function of the glancing angle q; LiF (100)monocrystal as analyzer.

LEP_5_2 09.08.2007 12:18 Uhr Seite 245

246 PHYWE Systeme GmbH & Co. KG · 37070 GöttingenLaboratory Experiments Physics

5.4.06-00 Monochromatization of copper X-rays


Principle:Polychromatic X-rays are to be ener-gy analyzed using various monocrys-tals and a suitably selected thinmetal foil having an absorption edgewhich drastically reduces the inten-sity of an unwanted line.

Copper X-ray monochromatization with Ni filter; LiF (100) monocrystal as an-alyzer (Diameter of diaphragm tube d = 2 mm).


What you need:


ted by the copper anode is to begraphically recorded as a functionof the Bragg angle, using LiF andKBr monocrystals successively asanalyzers.

2. The energy values of the charac-teristic copper lines are to be cal-culated.

3. The LiF monocrystal is to be usedto filter out a characteristic lineand the appertaining monochrom-atization graphically recorded.

4. Step 1 is to be repeated, using anickel filter.

� Bremsstrahlung� Characteristic radiation� Energy levels� Absorption� Absorption edges� Interference� Diffraction� Bragg scattering







Diaphragm tube with Ni- foil 09056.03 1





or




Complete Equipment Set, Manual on CD-ROM includedMonochromatization of copper X-rays P2540600

Copper X-ray intensity as a function of the glancing angle q; LiF (100)monocrystal as analyzer (Diameter of diaphragm tube d = 1 mm).

LEP_5_2 09.08.2007 12:18 Uhr Seite 246

L

What you need:

Complete Equipment Set, Manual on CD-ROM included20000

247PHYWE Systeme GmbH & Co. KG · 37070 Göttingen Laboratory Experiments Physics


Ka doublet splitting of molybdenum X-rays / fine structure 5.4.07-00


Principle:The polychromatic molybdenum X-rayspectrum is to analyzed by means ofa monocrystal. The energy of thecharacteristic lines is to be deter-mined from the positions of theglancing angles at various orders ofdiffraction. The separation of the Kadoublet in higher order diffraction isto be examined.

X-ray spectrum of molybdenum; separation of the Ka1 and Ka2 lines in 5th

order diffraction.


ted by the molybdenum anode atmaximum anode voltage is to berecorded as a function of theBragg angle, using an LiFmonocrystal as analyzer.

2. The wavelengths and ratio of theintensities of the two Ka lines areto be determined in high orderdiffraction, and a comparisonmade with the theoretical predic-tions.

� Characteristic X-ray radiation� Energy levels� Selection rules� The Bragg equation� Energy term symbols










or




What you need:

Complete Equipment Set, Manual on CD-ROM includedKa doublet splitting of molybdenum X-rays / fine structure P2540700

LEP_5_2 09.08.2007 12:18 Uhr Seite 247


5.4.08-00 Ka doublet splitting of iron X-rays / fine structure

Principle:The polychromatic iron X-ray spec-trum is to analyzed by means of amonocrystal. The energy of the char-acteristic lines is to be determinedfrom the positions of the glancingangles for various orders of diffrac-tion. The separation of the Ka dou-blet in higher order diffraction is tobe examined.

X-ray spectrum of iron; separation of the Ka1 and Ka2 lines in 2nd orderdiffraction.


ted by the iron anode at maximumanode voltage is to be recorded asa function of the Bragg angleusing an LiF monocrystal as ana-lyzer.

2. The wavelengths and ratio of theintensities of the two Ka lines areto be determined in high orderdiffraction, and a comparisonmade with the theoretical predic-tions.










or




What you need:

Complete Equipment Set, Manual on CD-ROM includedKa doublet splitting of iron X-rays /fine structure P2540800



� Characteristic X-ray radiation� Energy levels� Selection rules� The Bragg equation� Energy term symbols

LEP_5_2 09.08.2007 12:18 Uhr Seite 248


Duane-Hunt displacement law and Planck's “quantum of action” 5.4.09-00


Principle:X-ray spectra are to be recorded as afunction of the anode voltage. Theshort wavelength limit of thebremsspectrum is to be used to de-termine the agreement with theDuane-Hunt displacement law, andto determine Planck's “quantum ofaction”.

Bremsstrahlung as function of two anode voltages; Glancing angle q as x-axis in degree.


ted by the copper anode at variousanode voltages is to be recordedas a function of the Bragg angle,using an LiF monocrystal.

2. The short wavelength limit(=maximum energy) of the brems-spectrum is to be determined forthe spectra obtained in (1).

3. The results are to be used to veri-fy the Duane-Hunt displacementlaw, and to determine Planck's“quantum of action”.


� X-ray tube� Bremsstrahlung� Characteristic X-ray radiation� Energy levels� Crystal structures� Lattice constant� Interference� The Bragg equation


Goniometer for X-ray unit, 35 kV 09058.10 1

Plug-in module with Cu X-ray tube 09058.50 1

Counter tube, type B, BNC cable, l = 50 cm 09005.00 1

Lithium fluoride crystal, mounted 09056.05 1





or




What you need:

Complete Equipment Set, Manual on CD-ROM includedDuane-Hunt displacement law andPlanck’s “quantum of action” P2540900

LEP_5_2 09.08.2007 12:18 Uhr Seite 249


5.4.10-00 Characteristic X-ray lines of different anode materials/Moseley's Law;Rydberg frequency and screening constant

20 30 40

10

15

20

Principle:The X-rays emanating from three X-ray tubes, each with a differentanode material, are to be analyzedand the wavelengths of the charac-teristic X-ray lines from each are tobe determined, so that Moseley'sLaw can be verified.

Moseley straight linesCurve a: Transition n2 —>n1 (Ka line)Curve b: Transition n3 —>n1 (Kb line)

Tasks:1. The X-ray spectra emanated from

Fe, Cu and Mo X-ray tubes are tobe recorded.

2. The Bragg angles of the character-istic lines are to be determinedfrom the spectra, and then be usedto determine their wavelengthsand frequencies.

3. The Rydberg constants and thescreening constants are to bedetermined from the Moseleystraight lines.












or

Software x-ray unit, 35 kV 14407.61 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristik X-ray lines of different anode materials / Moseley’s Law; Rydberg frequency and screening constant P2541000



� Characteristic X-ray radiation� Bohr's atomic model� Energy levels� Binding energy� Bragg scattering� Moseley's law; Rydberg

frequency and screeningconstant

Z

2f

108 s�1>2a

b

LEP_5_2 09.08.2007 12:18 Uhr Seite 250


Absorption of X-rays 5.4.11-00


1 0

10

8

8

7

2

1

3

7

6

6

9

9

4

4

3

3

2

2

1

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

5

5

Principle:Polychromatic X-rays are to be ener-gy selected using a monocrystal an-alyzer. The monochromatic radiationobtained is to serve as the primaryradiation source for examination ofthe absorption behaviour of variousmetals as a function of the absorberthickness and the wavelength of theprimary radiation.

3. The absorption coefficients forcopper and nickel are to be deter-mined as a function of the wave-length and the measured valuesplotted. The energies of the K lev-els are to be calculated.

4. The validity of m/r = f(Z3) is tobe proved.

Semi-logarithmic representation of the pulse rates as a function of the ab-sorber thickness.

Ua = 35 kV, Ia = 1 mA.

Curve 1: Al (Z = 13); l = 139 pm

Curve 2: Al (Z = 13); l = 70 pm

Curve 3: Zn (Z = 30); l = 139 pm.

Tasks:1. The intensity attenuation of the

primary radiation is to be mea-sured for aluminium and zinc as afunction of the material thicknessand at two different wavelengths.The mass absorption coefficientsare to be determined from thegraphical representation of themeasured values.

2. The mass absorption coefficientsfor aluminium, zinc and tin foils ofconstant thickness are to be de-termined as a function of thewavelength. It is to be shown fromthe graphical representation thatm/r = f(l3).


� Bremsstrahlung� Characteristic radiation� Bragg scattering� Law of absorption� Mass absorption coefficient� Absorption edges� Half-value thickness� Photoelectric effect� Compton scattering� Pair production






Absorption set for x-rays 09056.02 1

Software for X-ray Unit 35 kV 14407.61 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedAbsorption of X-rays P2541100

d/mm

I/I0

LEP_5_2 09.08.2007 12:18 Uhr Seite 251


5.4.12-00 K- and L-absorption edges of X-rays / Moseley's Law and the Rydberg constant

Principle:Samples of various elements of dif-ferent atomic numbers are to be irra-diated with X-rays of a known spec-tral distribution, and the energy ofthe transmitted intensities analyzedusing a monocrystal analyzer. TheRydberg constant and screeningconstants are to be found by deter-mining the energy at which absorp-tion edges occur.

3. The Rydberg and screening con-stants are to be calculated fromthe energy values of the K ab-sorption edges.

4. The L absorption edges of differ-ent absorber materials are to befound.

5. The Rydberg constant is to be cal-culated from the energy values ofthe L absorption edges.

X-ray spectra of copper without absorber and with K absorption edges forvarious absorbers.


ted from the copper anode is to berecorded as a function of theBragg angle using an LiFmonocrystal as analyzer.

2. The K absorption edges of differ-ent absorber materials are to befound.

X-ray basic unit, 35 kV 09058.99 1Goniometer for X-ray Unit 35 kV 09058.10 1Plug-in module with Cu-X-ray tube 09058.50 1Counter tube type B, BNC cable, l = 50 cm 09005.00 1Lithium fluorid crystal, mounted 09056.05 1Set of chemicals for edge absorption 09056.04 1Silver nitrate, cryst. 15 g 30222.00 1Mortar with pestle, 70 ml, porcelain 32603.00 1Spoon with spatula end, l = 150 mm, steel, micro 33393.00 1

Recording equipment:XYt recorder 11416.97 1Connecting cable, l = 100 cm, red 07363.01 2Connecting cable, l = 100 cm, blue 07363.04 2orSoftware x-ray unit, 35 kV 14407.61 1Data cable 2 x SUB-D, plug/socket, 9 pole 14602.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedK- and L-absorption edges of X-rays /Moseley’s Law and Rydberg constant P2541200



� X-ray bremsstrahlung� Characteristic radiation� Bragg equation� Bohr's atomic model� Atomic energy level scheme� Moseley's law� Rydberg constant� Screening constant

LEP_5_2 09.08.2007 12:18 Uhr Seite 252


Examination of the structure of NaCl monocrystals with different orientations 5.4.13-00


Principle:Polychromatic X-rays are to bedirected against NaCl monocrystalswith different orientations. Thespacing between the lattice planesof each monocrystals then to bedetermined by analyzing the wave-length-dependent intensity of thereflected radiation.

3. The planes of reflection and theirMiller indices are to be found.

X-ray intensity of copper as afunction of the glancing angle:

NaCl monocrystal with differentorientations as Bragg-analyzer:

1-(100); 2-(110); 3-(111)

Tasks:1. NaCl monocrystals with the orien-

tations (100), (110) and (111) areeach to be separately used torecord an intensity spectrum ofthe polychromatic radiation em-anated by the X-ray tube.

2. The Bragg angles of the character-istic radiations are to be deter-mined from the spectra, and thedistances between lattice planescalculated for each orientation.


� Characteristic X-ray radiation� Energy levels� Crystal structures� Reciprocal lattice� Miller indices� Bragg scattering� Atomic form factor� Structure factor





Universal crystal holder for X-Ray Unit 09058.02 1

NaCl-monocrystals, set of 3 09058.01 1





or




What you need:

Complete Equipment Set, Manual on CD-ROM includedExamination of the structure of NaCl monocrystalswith different orientations P2541300

LEP_5_2 09.08.2007 12:18 Uhr Seite 253

0

-yn-

-.

l.

.


5.4.14+15-00 X-ray investigation of different crystal structures / Debye-Scherrer powder method

Principle:Polycrystalline samples are to beirradiated by an X-ray beam and theresulting diffraction patterns record-ed on film and evaluated.

3. The lattice constants of the sam-ple materials are to be deter-mined.

4. The number of atoms in the unitcells of each sample are to be de-termined.

Debye-Scherrer pattern of a powdered sample of CsCl. Thickness of the sam-ple, 0.4 mm. Exposure time, 2.0 h. Mo X-ray tube: UA = 35 kV; IA = 1 mA.

Tasks:1. Debye-Scherrer photographs are

to be taken of powdered samplesof sodium chloride and caesiumchloride.

2. The Debye-Scherrer rings are to beevaluated and assigned to the cor-responding lattice planes.

Exp. P2542500 with hexagonal structuresExp. P2542400 with cubic structures

X-ray basic unit, 35 kV 09058.99 1 1

Plug-in module with Mo-X-ray tube 09058.60 1 1

Mortar with pestle, 70 ml, porcelain 32603.00 1



Caesium chloride 5 g 31171.02 1

Diaphragm tube with Zr- foil 09058.03 1

Vernier caliper, plastic 03011.00 1 1

Film holder 09058.08 1 1

Polaroid film (ISO 3000), 9 x 12 cm, 20 sheets 09058.20 1 1

Polaroid film holder chassis 09058.21 1 1

or

X-ray films, wet chemical, 100 x 100 mm, 100 pieces 09058.23 1 1

Bag for x-ray films, 10 pieces 09058.22 1 1

X-ray film developer, for 4.5 l solution 06696.20 1 1

X-ray film fixing, for 4.5 l solution 06696.30 1 1

Tray (PP), 180 x 240 mm, white 47481.00 3 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray investigation of different crystal structures /Debye-Scherrer powder method…of cubic crystal structures P2541400…of hexagonal crystal stuctures P2541500



� Crystal lattices� Crystal systems� Reciprocal lattice� Miller indices� Structure amplitude� Atomic form factor� Bragg scattering

Set-up of experiment P2541400

LEP_5_2 09.08.2007 12:18 Uhr Seite 254



X-ray investigation of crystal structures / Laue method 5.4.16-00

Principle:A monocrystal is to be irradiated by apolychromatic X-ray beam and theresulting diffraction patterns record-ed on film and evaluated.

Laue pattern of an LiF (100) crystal.

Cu X-ray tube: UA = 35 kV; IA = 1 mADistance between sample and film: D = 19 mmExposure time: t = 120 min

Tasks:1. The Laue diffraction of an LiF

monocrystal is to be recorded on afilm.

2. The Miller indices of the corre-sponding crystal surfaces are to beassigned to the Laue reflections.




Crystal holder for lane diffraction 09058.11 1

Film holder 09058.08 1


Polaroid film (ISO 3000), 9 x 12 cm, 20 sheets 09058.20 1

Polaroid film holder chassis 09058.21 1

or

X-ray films, wet chemical, 100 x 100 mm, 100 pieces 09058.23 1

Bag for x-ray films, 10 pieces 09058.22 1

X-ray film developer, for 4.5 l solution 06696.20 1

X-ray film fixing, for 4.5 l solution 06696.30 1

Tray (PP), 180 x 240 mm, white 47481.00 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray investigation of crystal structures /Laue method P2541600


� Crystal lattices� Crystal systems� Crystal classes� Bravais lattice� Reciprocal lattice� Miller indices� Structure amplitude� Atomic form factor� The Bragg equation

LEP_5_2 09.08.2007 12:18 Uhr Seite 255

5.4.17-00 Compton scattering of X-rays

55 60 65

0.35

0.4

0.3

0.25

0.2

Principle:Compton scattering is to be achievedby directing an X-ray beam against apiece of plastic. The portions of thescattered X-rays at various angles isto be measured with a counter tube.Measurements are to be made withan absorber positioned in front ofand behind the scatterer, so that theCompton wavelength can be deter-mined from the varying intensity at-tenuation of the X-rays at differentwavelengths, using a premeasuredtransmission curve.

for the same angles as previously,and the different transmission coef-ficients then calculated.

3. The different transmission coeffi-cients and the transmission curveare to be used to determine thechanges in wavelengths.

4. The Compton wavelength for 90°scattering is to be determined andcompared with the theoreticalvalue.

Transmission curve of aluminium.Experimental set-up for 90° Compton scattering.

Tasks:1. The transmission of an aluminium

absorber is to be determined as afunction of the wavelength of theX-rays by means of Bragg scatter-ing and the measured values plot-ted graphically.

2. A scatterer is to be used and theintensity of the X-rays scatteredat different angles determined.The intensity attenuation whichoccurs on placing an aluminiumabsorber in front of, and behind,the scatterer is to be determined


� Compton effect� Compton wavelength� Rest energy� Absorption� Transmission� Conservation of energy and

momentum� X-rays� The Bragg equation






Compton attachment for X-ray Unit 35 kV 09058.04 1

Software for X-ray Unit 35 kV 14407.61 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedCompton scattering of X-rays P2541700



Δl

l/pm

LEP_5_2 09.08.2007 12:18 Uhr Seite 256



X-ray dosimetry 5.4.18-00

3.0

2.0

1.0

100 200 300 400 500

Principle:The molecules of air within a platecapacitor are to be ionized by X-rays.The ion dose, ion dose rate and localion dose rate are to be calculatedfrom the ionization current and theradiated mass of air.

ous anode currents but with maxi-mum anode and capacitor voltages.

5. The saturation current is to beplotted as a function of the anodevoltage.

6. Using the d = 5 mm aperture, theion current is to be determinedand graphically recorded at vari-ous anode currents but with max-imum anode and capacitor volt-ages.

7. Using the two different diaphragmtubes and the fluorescent screen,the given distance between theaperture and the radiation sourceat maximum anode coltage andcurrent is to be verified.

Ionization current IC as a function of capacitor voltage UC for various anodevoltages UA. Diaphragm tube d = 5 mm; IA = 1 mA.

Tasks:1. The ion current at maximum

anode voltage is to be measuredand graphically recorded as afunction of the capacitor voltageby using two different beam limit-ing apertures.

2. The ion dose rate is to be deter-mined from the saturation currentvalues and the air masses pene-trated by radiation are to be cal-culated.

3. The energy dose rate and variouslocal ion dose rates are to be cal-culated.

4. Using the d = 5 mm aperture, theion current is to be determinedand graphically recorded at vari-



Capacitor plates for X-ray Unit 35 kV 09058.05 1


Direct current measuring amplifier 13620.93 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray dosimetry P2541800


� X-rays� Absorption inverse square law� Ionizing energy� Energy dose� Equivalent dose and ion dose

and their rates� Q factor� Local ion dose rate� Dosimeter

IC/nA

UC/V

UA= 35 kV

UA= 30 kV

UA= 25 kV

UA= 20 kV

UA= 15 kV

LEP_5_2 09.08.2007 12:18 Uhr Seite 257

5.4.19-00 Contrast medium experiment with a blood vessel model

Principle:A liquid contrast medium is to be in-jected into a model of a blood vessel,which is hidden from sight and ex-posed to X-ray radiation, to enablethe inner structure of the model tobe examined on a fluorescent screen.

Figure shows the model filled to different extents with contrast medium.

Experimental steps:1. A 50% potassium iodide solution

is to be injected into the bloodvessel model.

2. The fluorescent screen of the X-ray basic unit is to be observedto follow the course taken by theinjected solution in the blood ves-sel model.


� X-ray radiation� Bremsstrahlung� Characteristic radiation� Law of absorption� Mass absorption coefficient� Contrast medium



Blood vessel, model for contrast fluid 09058.06 1

Potassium iodide, 50 g 30104.05 1


Wide mouth bottle with screw cap, clear glass, 250 ml 46213.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedContrast medium experiment with a bood vessel model P2541900



LEP_5_2 09.08.2007 12:18 Uhr Seite 258



Determination of the length and position of an object which cannot be seen 5.4.20-00

Principle:The length and the spatial position ofa metal pin which cannot be seen areto be determined from radiograms oftwo different planes which are atright angles to each other.

Projection fotos of the implant model in the xz-plane (left) and in the yz-plane (right).

Tasks:1. The length of a metal pin which

cannot be seen is to be deter-mined from radiograms of twodifferent planes which are at rightangles to each other.

2. The true length of the pin is tobe determined by taking themagnification which results fromthe divergence of the X-rays intoaccount.

3. The spatial position of the pin is tobe determined.



Film holder 09058.08 1

Implant model for X-ray photography 09058.07 1


Polaroid film (ISO 3000), 9 x 12 cm, 20 sheets 09058.20 1

Polaroid film holder chassis 09058.21 1

or

X-ray films, wet chemical, 100 x 100 mm, 100 pieces 09058.23 1

Bag for x-ray films, 10 pieces 09058.22 1

X-ray film developer, for 4.5 l solution 06696.20 1

X-ray film fixing, for 4.5 l solution 06696.30 1

Tray (PP), 180 x 240 mm, white 47481.00 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedDetermination of the length and position of an object which cannot be seen P2542000


� X-ray radiation� Bremsstrahlung� Characteristic radiation� Law of absorption� Mass absorption coefficient� Stereographic projection

LEP_5_2 09.08.2007 12:18 Uhr Seite 259



5.4.21/22/23/24/25 Diffractometric Debye-Scherrer patterns of different powder samples

Principle:Polycrystalline powder samples,which crystallize in the three cubicBravais types, simple, face-centeredand body-centered, are irradiatedwith the radiation from a Roentgentube with a copper anode. A swivel-ling Geiger-Mueller counter tube de-tects the radiation that is construc-tively reflected from the various lat-tice planes of the crystallites. TheBragg diagrams are automatically

recorded. Their evaluation gives theassignment of the Bragg lines to theindividual lattice planes, their spac-ings as well as the lattice constantsof the samples, and so also the cor-responding Bravais lattice type.

Problems:1. Record the intensity of the Cu

X-rays back scattered by the fourcubic crystal powder samples withvarious Bravais lattice types as afunction of the scattering angle.

Bragg-Cu-Ka and Cu-Kb-lines of NH4Cl.

2. Calculate the lattice plane spac-ings appropriate to the angularpositions of the individual Bragglines.

3. Assign the Bragg reflections to therespective lattice planes. Deter-mine the lattice constants of thesamples and their Bravais latticetypes.

4. Determine the number of atoms inthe unit cell.

Exp. P2542500 with a cubic powder sampleExp. P2542400 with a tetragonal lattice structureExp. P2542300 with a hexagonal lattice structureExp. P2542200 with diamond structureExp. P2542100 with the three cubic Bravais lattices

X-ray basic unit, 35 kV 09058.99 1 1 1 1 1Goniometer for X-ray Unit 35 kV 09058.10 1 1 1 1 1Plug-in module with Cu-X-ray tube 09058.50 1 1 1 1 1Counter tube type B, BNC cable, l = 50 cm 09005.00 1 1 1 1 1Lithium fluorid crystal, mounted 09056.05 1 1 1 1 1Universal crystal holder for X-Ray Unit 09058.02 1 1 1 1 1Probe holder for powder probes (diffractometry) 09058.09 1 1 1 1 1Diaphragm tube with Ni- foil 09056.03 1 1 1 1 1Spoon with spatula end, l = 150 mm, steel, micro 33393.00 1 1 1 1 1Vaseline, 100 g 30238.10 1 1 1 1 1Mortar with pestle, 70 ml, porcelain 32603.00 1 1 1Ammonium chloride, 250 g 30024.25 1Potassium chloride, 250 g 30098.25 1Potassium bromide 100 g 30258.10 1Molybdenum, Powder, 99,7%, 100 g 31767.10 1Germanium, Powder, 99%, 10 g 31768.03 1Silicium, Powder, 50 g 31155.05 1Zinc, powder 100 g 31978.10 1Lead-IV oxide, lead diox., 250 g 31122.25 1Sodium chloride, 250 g 30155.25 1Software for X-ray Unit 35 kV* 14407.61 1 1 1 1 1Data cable 2 x SUB-D, plug/socket, 9 pole* 14602.00 1 1 1 1 1PC, Windows® 95 or higher*

*Alternatively:Xyt recorder 11416.97 1 1 1 1 1Conn. cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 1 1 1 1 1Conn. cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 1 1 1 1 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffractometric Debye-Scherrer patterns of differentpowder samples P254 21/22/23/24/25-00


� Wavelength� Crystal lattices� Crystal systems� Bravais-lattice� Reciprocal lattice� Miller indices� Structure factor� Atomic scattering factor� Bragg scattering� Characteristic X-rays� Monochromatization

of X-rays

LEP_5_2 09.08.2007 12:18 Uhr Seite 260


Diffractometric measurements to determine the intensity of Debye-Scherrer reflexes 5.4.26-00using a cubic lattice powder sample


Principle:A polycrystalline, cubic face-cen-tered crystallizing powder sample isirradiated with the radiation from aX-ray tube with a copper anode. AGeiger-Mueller counter tube is auto-matically swivelled to detect the ra-diation that is constructively reflect-

ed from the various lattice planes ofthe crystallites. The Bragg diagram isautomatically recorded. The intensi-ties of the individual reflex lines aredetermined and compared withthose theoretically expected. In ad-dition, the evaluation allows theBragg reflexes to be assigned to theindividual lattice planes, and boththeir spacing and the correspondingBravais lattice type to be deter-mined.

Debye-Scherrer pattern of a copper powder sample.

Tasks:1. Record the intensity of the Cu

X-rays back scattered by a cubic-crystallizing copper powder sam-ple as a function of the scatteringangle.


� Crystal lattices� Crystal systems� Bravais-lattice� Reciprocal lattice� Miller indices� Structure factor� Atomic scattering factor � Lorentz-polarization factor� Multiplicity factor� Debye-Waller factor� Absorption factor� Bragg scattering� Characteristic X-rays� Monochromatization

of X-rays

X-ray basic unit, 35 kV 09058.99 1Goniometer for X-ray Unit 35 kV 09058.10 1Plug-in module with Cu-X-ray tube 09058.50 1Counter tube type B, BNC cable, l = 50 cm 09005.00 1Lithium fluorid crystal, mounted 09056.05 1Universal crystal holder for X-Ray Unit 09058.02 1Probe holder for powder probes (diffractometry) 09058.09 1Diaphragm tube with Ni- foil 09056.03 1Spoon with spatula end, l = 150 mm, steel, micro 33393.00 1Vaseline, 100 g 30238.10 1Copper, powder, 100 g 30119.10 1Software for X-ray Unit 35 kV* 14407.61 1Data cable 2 x SUB-D, plug/socket, 9 pole* 14602.00 1PC, Windows® 95 or higher

*Alternatively:Xyt recorder 11416.97 1Connecting cable, 4 mm plug, 32 A, red, l = 100 cm 07363.01 1Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm 07363.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffractometric measurements to determine the intensity of Debye-Scherrer reflexes using a cubic lattice powder sample P2542600

2. Calculate the lattice plane spac-ings from the angle positions ofthe individual Bragg lines.

3. Assign the Bragg reflexes to therespective lattice planes. Calculatethe lattice constant of the sub-stance and the Bravais lattice type.

4. Determine the intensity of the in-dividual reflex lines and comparethem with the theoretically ex-pected intensities.

5. Determine the number of atoms inthe unit cell.

LEP_5_2 09.08.2007 12:18 Uhr Seite 261


What you need:

5.4.27-00 Diffractometric Debye-Scherrer measurements for the examination of the texture of rolled sheets

Principle:A polycrystalline, cubic face-cen-tered crystallizing copper powdersample and a thin copper sheet areseparately irradiated with the radia-tion from a X-ray tube with a copperanode. A Geiger-Mueller counter

tube is automatically swivelled todetect the radiation that is construc-tively reflected from the various lat-tice planes of the crystallites. TheBragg diagrams are automaticallyrecorded. The evaluation allows theBragg reflexes to be assigned to theindividual lattice planes. In contrastto the powder sample, the rolled thinsheet gives a spectrum showing analignment of the crystallites (rolledtexture), that is made even morecomplete by heating the sheet.

Debye-Scherrer diagram of a rolled copper sheet.

Tasks:1. Record the intensity of the Cu X-

rays back scattered by a cubiccrystallizing copper powder sam-ple as a function of the scatteringangle.

2. Assign the Bragg reflexes to theindividual lattice planes.

3. Record the Bragg spectrum of athin sheet of copper.

4. Repeat the measurements made inTask 3 after the sheet of copperhas been subjected to annealing.






Universal crystal holder for X-Ray Unit 09058.02 1

Probe holder for powder probes (diffractometry) 09058.09 1

Diaphragm tube with Ni- foil 09056.03 1


Vaseline, 100 g 30238.10 1

Copper, powder, 100 g 30119.10 1

Copper foil, 0.1 mm, 100 g 30117.10 1

Crucible tongs, 200 mm, stainless steel 33600.00 1

Butane burner for cartridge 270 and 470 47536.00 1

Butane cartridge 47535.00 1

Software for X-ray Unit 35 kV* 14407.61 1

Data cable 2 x SUB-D, plug/socket, 9 pole* 14602.00 1


*Alternatively:

Xyt recorder 11416.97 1



Complete Equipment Set, Manual on CD-ROM includedDiffractometric Debye-Scherrer measurements for theexamination of the texture of rolled sheets P2542700



� Wavelength� Crystal lattices� Crystal systems� Bravais-lattice� Reciprocal lattice� Miller indices� Structure factor� Atomic scattering factor � Bragg scattering� Characteristic X-rays� Monochromatization

of X-rays� Fiber textures� Sheet textures� Annealing texture� Recrystallization

LEP_5_2 09.08.2007 12:18 Uhr Seite 262


Characteristic X-rays of tungsten 5.4.28-00


Principle:Spectra of X-rays from a tungstenanode are to be analyzed by meansof a LiF monocrystal and the resultsplotted graphically. The energies ofthe characteristic lines are then to bedetermined from the positions of theglancing angles for the various or-ders of diffraction. As the necessaryenergy for the k-transition (69,5 keV)is higher than the applied energy in

this experiment, the transition takesplace in lower level l, m and even oshell. The identification of the differ-ent transitions is a major task in thisexperiment.

X-ray intensity of tungsten as a function of the glancing angle; a LiF (100)monocrystal is used as a Bragg analyser..


ted by the tungsten anode atmaximum anode voltage andanode current is to be recorded asa function of the Bragg angle,using an LiF monocrystal as ana-lyzer.

2. The energy values of the charac-teristic tungsten lines are to becalculated and compared with theenergy differences of the copperenergy terms

3. The identification of the various l- lines has to be carried out byapplying the appropriate selectionrules.


� Bremsstrahlung� Characteristic radiation� Energy levels� Crystal structures� Lattice constant� Absorption� Absorption edges� Interference� The Bragg equation� Order of diffraction� L-Transition


Goniometer for X-ray unit, 35 kV 09058.10 1

Plug-in module with W X-ray tube 09058.80 1

Counter tube, type B 09005.00 1

Lithium fluoride crystal, mounted 09056.05 1





or


RS232 data cable 14602.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristic X-rays of tungsten P2542800

LEP_5_2 09.08.2007 12:18 Uhr Seite 263


5.4.40-00 Spectroscopy with the X-ray energy detector

Principle:The X-ray energy detector is used togain information about the energydistribution of high energy gammaradiation in the range of 2 to 40 keV.The X-ray energy detector with a res-olution of 380 keV in combinationwith a multi channel analyzer is usedfor direct measurement of the tran-sition energies of K and L levels ofmetals and alloys.

Spectrum of a Gold/Silver alloy

Tasks:1. Calibration of the X-ray energy

spectrum of copper

2. Determination of the resolution ofthe X-ray energy detector

3. X-ray fluorescence analysis ofpure metals and alloys

4. Verification of the Bragg equationwith the help of the X-ray energydetector


Goniometer for X-ray unit 35 kV 09058.10 1

Plug-in Cu tube for X-ray unit 09058.50 1

X-ray energy detector 09058.30 1



Specimen set X-ray energy detector 09058.31 1

Univ. crystal holder 09058.02 1

Probe holder for powder probes 09058.09 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedSpectroscopy with the X-ray energy detector P2544000



� Energy levels � Bremsstrahlung� Characteristic radiation� Bragg equation� Selection rules

LEP_5_2 09.08.2007 12:18 Uhr Seite 264



1 (25401)Characteristic X-rays of copper2 (25402)Characteristic X-rays of molybdenum3 (25403)Characteristic X-rays of iron4 (25404)The intensity of characteristic X-rays as a function of anodecurrent and anode voltage5 (25405)Monochromatization of molybdenum X-rays6 (25406)Monochromatization of copper X-rays7 (25407)K� doublet splitting of molybdenumX-rays / fine structure8 (25408)K� doublet splitting of iron X-rays / fine structure9 (25409)Duane-Hunt displacement law andPlanck's “quantum of action”10 (25410)Characteristic X-ray lines of differ-ent anode materials/ Moseley's Law;Rydberg frequency and screeningconstant11 (25411)Absorption of X-rays12 (25412)K and L absorption edges of X-rays /Moseley's law and the Rydbergconstant13 (25413)Examination of the structure ofNaCl monocrystals with differentorientations14 (25414)X-ray investigation of cubic crystalstructures / Debye-Scherrer powdermethod15 (25415)X-ray investigation of hexagonalcrystal structures / Debye-Scherrerpowder method

16 (25416)X-ray investigation of crystalstructures / Laue method17 (25417)Compton scattering of X-rays18 (25418)X-ray dosimetry19 (25419)Contrast medium experiment with ablood vessel model20 (25420)Determination of the length andposition of an object which cannotbe seen21 (25421)Diffractometric Debye-Scherrerpatterns of powder samples withthe three cubic Bravais lattices22 (25422)Diffractometric Debye-Scherrerpatterns of powder samples withdiamond structure (germanium andsilicon)23 (25423)Diffractometric Debye-Scherrerpatterns of powder samples with ahexagonal lattice structure24 (25424)Diffractometric Debye-Scherrerpatterns of powder samples with atetragonal lattice structure25 (25425)Graphical evaluation of a diffracto-metric Debye-Scherrer patterns of acubic powder sample26 (25426)Diffractometric measurements todetermine the intensity of Debye-Scherrer reflexes using a cubiclattice powder sample as example

27 (25427)Debye-Scherrer diffractometricmeasurements for the examinationof the texture of rolled sheets

A unique feature:3 different X-ray tubes with anodes made of copper or molybdenum or iron to beplugged into the unit.Due to their anode material, the tubes show different characteristic X-ray lines (Moseleylaw). They can thus be used for fundamental measurements concerning the formation of X-rays and also for experiments on the basis of radiation of different hardness levels (wavelength). The X-ray tubes are separately available and easy to exchange:

The tubes are completely adjusted and come supplied in separate plug-in modules which aresimply to be plugged into the basic unit. Exchanging the tubes takes only seconds and theX-ray unit is immediately ready to operate.

Further new features:● RS232 interface for computer-assisted control, measuring and evaluation purposes

● X-ray tube visible during operation

● integrated rate meter with counter

X-Ray Experiments

X-Ray Experiments • No. 01189.02 • 27 described ExperimentsPlease ask for a complete equipment list Ref. No. 25421

Contrast medium experiment with a blood vessel model

Models for two different extent with contrast medium

LEP_5_2 09.08.2007 12:18 Uhr Seite 265


Handbooks


Please ask for a completeequipment list Ref. No.25422

1. Mechanics1.1 (13301)Frequency of a spring pendulum1.2 (13302)Frequency of a thread pendulum1.3 (13369)Free fall with a screen1.4 (13370)The path-time law for free fallwith the falling sphere apparatus1.5 (13371)Uniform, linear, unacceleratedmotion1.6 (13372)Force-free, linear motion1.7 (13373)Uniformly accelerated, linear mo-tion, Newton`s 2nd law1.8 (13374)The elastic collision1.9 (13375)The inelastic collision1.10 (13376)Frequency of a thread pendulum1.11 (13377)Pendulum oscillations-variable g pendulum1.12 (13378)The harmonic oscillation of heli-cal springs-parallel and seriesconnection of spring1.13 (13379)Dependence of the oscillation pe-riod of a leaf spring on the pen-dulum length & pendulum mass1.14 (13380)Moment of inertia of differentbodies:disc,solid and hollowcylinder - Steiner`s law1.15 (13381)Uniform rotary motion1.16 (13382)Uniform, accelerated rotationalmotion, moment of inertia

2. Acoustics2.1 (13360)Measurement of frequency oftuning forks, detuning of tuningforks2.2 (13361)Investigation of the naturaloscillation of columns of air2.3 (13362)Measurement of the speed ofsound in air2.4 (13363)Measurement of the speed ofsound in diffent gases2.5 (13364)Measurement of the speed inmetal rods2.6 (13365)Acoustical Doppler effect2.7 (13615)Investigation of beats2.8 (13619)Influence of damping on thespectrum of the characteristicoscillations of air columns2.9 (13620)Characteristic oscillations in cavityresonators - Hemholtz's resonators2.10 (13621)Tone analysis

2.11 (13622)Oscillations in metal plates2.12 (13623)Speech analysis2.13 (13628)Signal filtration - elimination ofbackground noises2.14 (13629)Determination of the speed ofsound in air - travel time measure-ment between two microphones2.15 (13630)Acoustic spacial orientation

3. Thermodynamics3.1 (13491)Specific heat capacity of water3.2 (13492)Specific evaporation heat ofwater3.3 (13493)Specific heat capacity of liquids3.4 (13494)Specific heat capacity of solidbodies3.5 (13495)Specific condensation heat ofwater3.6 (13496)Specific melting heat of ice3.7 (13497)Specific dissolution heat of salts3.8 (13498)Specific heat value of fuels3.9 (13499)Volume expansion of gases3.10 (13500)Gay-Lussas Law3.11 (13501)Amontons Law3.12 (13502)Boyle's and Mariotte's Law3.13 (13641)Gay-Lussac's law3.14 (13642)Charles' (Amontons') law - variant A3.15 (13643)Charles' (Amontons') law - variant B3.16 (13644)Boyle and Mariotte's law

4 Electricity4.1 (13303)Ohm's Law4.2 (13304)Temperature dependence of theresistance of pure metals4.3 (13305)Characteristics of semi-conductordiodes4.4 (13306)Collector current-collector voltagecharacteristic of an NPN-transistor4.5 (13307)Second order conductors4.6 (13308)Switch-on current of aincandescent bulb4.7 (13309)Measurement of the work andpower of an incandescent bulb4.8 (13310)Switch-on behaviour of acapacitance4.9 (13311)Switch-on behaviour of aninductivity4.10 (13312)Induction impulse



1. Food Chemistry1.1 (13705)The manual titration of citric acid1.2 (13706)The automatic titration of ordinary vinegar1.3 (13707)Determination of the phosporic acid contentof a soft drink1.4 (13708)The pH and degree of acidity of coffee1.5 (13709)Determination of the content of fruit acidin juices and wine1.6 (13710)Titration curves of fresh milk and sour milk1.7 (13711)Changes in pH during the aging of milk(souring)1.8 (13712)The buffering properties of foods1.9 (13713)Determination of the calcium carbonatecontent of egg shell1.10 (13714)Determination of the common salt contentof meat broth1.11 (13715)Chloride in mineral water

2 Ecology and Environment2.1 (13701)The conductivity of various water samples2.2 (13702)The pH of various water samples2.3 (13703)The origin of acid rain2.4 (13704)The twenty-four hour rhythm of an aquaticplant2.5 (13509)Comparison of the heat capacities of waterand land2.6 (13510)The Bergman rule: heat loss in dependenceon body surface area and volume2.7 (13511)The isolating effect of body coverage2.8 (13325)Daily course of luminosity2.9 (13325)Daily course of luminosity

3. Biochemistry3.1 (13696)Determination of the isoelectric point of anamino acid (glycine)3.2 (13697)The ionic permeability of the cell membrane3.3 (13698)Determination of the Michaelis constant3.4 (13699)Substrate inhibition of enzymes3.5 (13700)Enzyme inhibition (poisoning of enzymes

4. Nerves Physiology4.1 (13600)Neuro-simulator (membrane time constantand low-pass filtering)4.2 (13601)Neuro-simulator (how an exciting synapsefunctions)4.3 (13602)Mechanical stimulation of the rear end ofan earthworm4.4 (13603)Mechanical stimulation of the front end ofan earthworm4.5 (13604)Electrical stimulation of an anaesthesizedearthworm

5. Human Physiology5.1 (13326)Cardiac and vasular sonic measurement(Phonocardiography)5.2 (13327)Electrocardiography5.3 (13327)Electrocardiography5.4 (13503)Electromyography5.5 (13605)Muscle stretch reflex and determination ofconducting velocity5.6 (13504)Electro-oculography5.7 (13326)Cardiac and vascular sonic measurement(Phonocardiography)5.8 (13606)Acoustic orientation in space5.9 (13607)The enzymatic activity of catalase5.10 (13505)Blood pressure measurement5.11 (13506)Measurement of the respiratory rate5.12 (13507)Changes in the blood flow during smoking5.13 (13508)Regulation of body temperature

6. Plant Physiology6.1 (13608)Photosynthesis (bubble-counting method)6.2 (13513)Photosynthesis (measurement of oxygenpressure)6.3 (13512)Transpiration of leaves6.4 (13609)Glycolysis (measurement of pressure)6.5 (13514)Glycolysis (measurement of temperature6.6 (13515)Calorimetry of foods

7. Electrochemistry7.1 (13318)Electrolysis of copper sulphate solutions7.2 (13319)The electrochemical series of metals7.3 (13320)Electric potential of a concentrationelement

8. Chemical equilibrium8.1 (13321)Chromatographic seperation processes: gas chromatography

9. Gas laws9.1 (13499)Volume expansion of gases (with Software Pressure)9.2 (13500)Gay-Lussas Law (with Software Pressure)9.3 (13501)Amontons Law (with Software Pressure)9.4 (13502)Boyle's and Mariotte's Law (with Software Pressure)9.5 (13641)Gay-Lussac's law (with Software Gas Laws)9.6 (13642)Charles' (Amontons') law - variant A (with Software Gas Laws)9.7 (13643)Charles' (Amontons') law - variant B (with Software Gas Laws)9.8 (13644)Boyle and Mariotte's law (with Software Gas Laws)

Interface-System Cobra3 Physics, Chemistry /Biology

Cobra3 Physics • No. 01310.02

Cobra3 Chemistry/Biology • No. 01320.02

4.11 (13313)Generation of an alternating cur-rent, rectification and filtration4.12 (13314)Efficiency of motor and generator4.13 (13366)Measurement of the reboundtime of a switch4.14 (13367)Current-voltage characteristic ofa solar cell4.15 (13611)Single-valued and multiple-valued Fourier spectra4.16 (13612)Analysis of simple and compositesinusoidal signals4.17 (13613)Spectral analysis of differentsignal forms - sinusoidal, rectan-gular, triangular signals4.18 (13614)Spectral analysis of periodic spikepulses4.19 (13616)Determination of the non-lineardistortion factor from the Fourierspectrum of distorted sinusoidaloscillations4.20 (13617)The Fourier spectrum of rectified,non-smoothed alternating currents4.21 (13618)Investigation of the characteristicoscillations of air columns4.22 (13624)Coupled electrical resonant cir-cuits4.23 (13625)Forced oscillations of a non-linearelectrical series resonance circuit- chaotic oscillation4.24 (13626)Analysis of Fourier series4.25 (13627)High-pass, low-pass, bandpassfilters4.26 (13631)Switch rebound4.27 (13632)Phase relationships in a seriesresonant circuit4.28 (13633)Free damped oscillation

5. Optics5.1 (13315)Dependence of the luminousintensity on the distance

6. Physical Structure of Matter6.1 (13368)Franck-Hertz Experiment6.2 (13634)Range of alpha particles in the air6.3 (13635)Mean range of beta radiation in air6.4 (13636)Absorption of electrons (orpositrons) in thin layers of matter6.5 (13637)The quantal flux of gammaradiation in air6.6 (13638)Absorption of gamma quanta (or electrons) as a function ofmaterial density6.7 (13639)Law of radioactive decay6.8 (13640)Radioactive equilibrium

LEP_5_2 09.08.2007 12:18 Uhr Seite 266

Index



Index

A�-, �-, �-particles 219

�-energies of 226Ra 223

�-particles in gases 224

�-spectrum of 241Am 222

Absorption 145, 199, 207, 241242, 243, 245, 246

256, 263

Absorption coefficient of ultrasonic waves 73

Absorption coefficient 227, 228

Absorption edges 241, 242, 243245, 246, 251

263

Absorption edges of X-rays 252

Absorption factor 261, 262

Absorption inversesquare law 257

Absorption of gamma or beta rays 227

Absorption of X-rays 251

AC circuit 185, 186, 192

AC impedance 185, 186

Acceleration 19, 20

Acceleration due to gravity 19, 24

Acceptors 161, 162

Acoustic Doppler effect 63

Acoustic resonant circuit 67

Acoustic waves 68

Adhesion 57

Adiabatic coefficient of gases 134

Adsorption 208

Advanced Optics 123

Aerofoil 60

Air track 19, 20, 21, 22

Airy disk, Airy ring 101

Amonton’s law 128, 149

Amplitude holograms 114

Amplitude 36, 66

Analyzer 108, 111

Angle of incidence 60

Angle of scattering 221

Angular acceleration 28, 29, 3033, 40, 41

Angular frequency 43, 44

Angular momentum 27, 30, 3435, 209, 211

Angular restoring force 45, 46

Angular restoring moment 48

Angular restoring torque 47

Angular velocity 28, 29, 30, 3132, 33, 4041, 47, 54

Anode 207

Anomalous Hall effect 236

Antineutrino 227

Aperiodic case 43, 44

Apparent force 31, 32

Are discharge 239

Atomic beam 213

Atomic energy level scheme 252

Atomic form factor 253, 254, 255

Atomic model accordingto Bohr 210

Atomic scattering factor 260, 261 262

Atomic spectra 211

Attenuation coefficient 225

Avalanche effect 157, 188

Average velocity 132

Avogadro’s law 149

Avogadro’s number 164

Axis of rotation 45, 46, 48

B�-deflection 219

�-decay, rays 226, 227

�-spectroscopy 226

Babinet’s theorem 76, 101, 104

Ballistic Pendulum 27

Ballistics 26

Balmer series 210

Band gap 237, 238

Band-pass filter 194

Band spacing 233, 234

Band theory 233, 234, 235237, 238

Band-width 187, 194

Barometric height formula 59

Barrier layer 130, 223

Basic constants 13

Beat 40, 41

Beat frequency 63

Bernoulli equation 60

Bessel function 76, 101

Bethe formula 224

Binding energy 210, 232, 250

Biot-Savart’s law 175, 176

Birefraction 113

Birefringence 117

Black body radiation 143

Blood vessel model 258

Bode diagram 190

Bohr magneton 212, 213

Bohr’s atomic model 212, 250, 252

Boiling point 136, 137, 139

Boiling point elevation 141

Bounding surface 58

Boyle and Mariotte’s law 128, 149

Boyle temperature 133

Bragg equation 241, 242, 243244, 247, 248

249, 252, 255, 256, 264

Bragg reflection 215

Bragg scattering 245, 246, 250251, 253, 254260, 261, 262

Bravais lattice 255, 260, 261, 262

Bremsstrahlung 241, 242, 243245, 246, 249251, 258, 259

263, 264

Brewster angle 115, 117

Brewster’s law 110, 111

Broadening of lines due toDoppler effect and pressurebroadening 97

CCapacitance 169, 172, 186

187, 190, 192

Capacitance of a platecapacitor 173

Capacitance of metal spheres 169

Capacitor 166, 167, 168169, 187, 190

Capacitor in the AC circuit 186

Carbon film resistor 157

Cardanic gyroscope 35

Carnot cycle 139

Cathode 207

Cathode rays 204

Cavendish balance 25

Cavity resonator 67

Central force 221

Centre of gravity 45, 46

Centrifugal force 31, 32, 54

Centripetal force 31, 32

Characteristic curves 162

Characteristic curves of semiconductors 162

Characteristic frequency 40, 4143, 44

Characteristic impedance 194

Characteristic radiation 241, 242243, 245, 246251, 252, 258

259, 263, 264

Characteristic X-ray lines of different anode materials 250

Characteristic X-rays of copper 241

Characteristic X-rays of iron 243

Characteristic X-rays of molybdenum 242

Characteristic X-rays of tungsten 263

Characteristic X-rays 241, 242243, 244

260, 261, 262

Characteristic 230, 232, 244X-ray radiation 247, 248, 249

250, 253

Charge 164, 169

Charge carrier generation 157

Charge carriers 236

Charging 167, 168

Charging capacitor 188

Charles’ (Amontons’) law 128

Chemical potential 141, 142

Chladni figures 64

Circuit 155, 190

Circular motion 30

Circularly and ellipticallypolarised light 108

Circularly and ellipticallypolarized waves 197

Circulation 60

Clausius-Clapeyronequation 139, 140

Cloud Chamber 219

CO2-laser 115



Damping 187

Damping constant 43, 44

Damping of waves 49

Daughter substance 210, 216217,

De Broglie equation 215

De Broglie relationship 99

De Broglie wavelength 229

Dead time 218, 227

Debye temperature 136, 137

Debye-Scherrer measurements 262

Debye-Scherrer method 215

Debye-Scherrer patterns 260

Debye-Scherrer powdermethod 254

Debye-Scherrer reflexes 261

Debye-Sears-effect 122

Debye-Waller factor 261, 262

Decay constant 216, 217

Decay diagram 226

Decay energy 130, 223, 226

Decay series 130, 219, 223

Decomposition of force 38, 39

Decomposition voltage 163

Defect electrons 236

Deformation 15

Degree of dissociation 141, 142

Degree of freedom 130

Demonstration experiments 85, 86124, 149

200

Demonstration track 19, 20, 21, 22

Density 71, 225

Density of liquids 53

Dependency of wave velocity 51

Detection probability 231

Developing of film 114

Diameter 13

Dielectric barrier 239

Dielectric constant 173

Dielectric displacement 170, 171173

Dielectric polarisation 173

Dielectrics 169

Differencial energy loss 224

Differentiating network 181

Different symmetriesof distributions 218

Diffraction 52, 68, 74, 75, 7677, 82, 99, 100

101, 102, 103, 104114, 196, 197, 245

246

Diffraction at the slit 196

Diffraction imageof a diffraction grating 210

Diffraction of microwaves 196

Diffraction index 181

Diffraction spectrometer 209

Diffraction uncertainty 99

Diffractometric Debye-Scherrermeasurements 261, 262

Diffractometric Debye-Scherrer patterns 260

Diffractometric measurements 261

Diffusion 144

Diffusion cloud chamber 219

Diffusion potential 161

Diode and Zener diode 188

Diode laser 118, 120

Direct energy conversion 159

Directional characteristicpattern 198

Directional quantization 213

Directivity 198

Discharging 167, 168

Disintegration product 216, 217

Dispersion 91

Dissipation factor 194

Donors 161, 162

Doppler effect 52, 6383, 116

Doppler shift of frequency 63, 83

Dosimeter 257

Double refraction 108

Double slit 74, 103

Doublets 209

Drag 60

Drag coefficient 60

Droplet method 203

Du Nouy method 57

Duane-Huntdisplacement law 249

Dulong Petit’s law 136, 137

Duration 230

Cobra3 266

Coefficient of cubiccompressibility 128

Coefficient of thermalexpansion 128

Coefficient of thermal tension 128

Coercive field strength 180

Coherence 95, 97, 101102, 103, 104, 114

Coherence conditions 97

Coherence length fornon punctual light sources 97

Coherence time 97

Coherent light 93

Coil 182, 183, 187, 190

Coil in the AC circuit 185

Collector equations 145

Collision of second type 117

Compressibility 71

Compressor 146

Compton effect 227, 229, 231246, 256

Compton scattering 228, 231251

Compton scattering of X-rays 256

Compton wavelength 229, 256

Concave lens 51, 90

Concentration ratio 141, 142

Condensation 146

Conduction band 161, 162, 233234, 235, 237

238

Conduction of heat 145

Conductivity 153, 154, 165233, 234

Conductivity of metals 144

Conductor 155, 165

Conductor (Magnetic field) 179

Connection between the finestructure of the �-spectrumand the accompanying�-spectrum 222

Conservation of angularmomentum 227

Conservation of energy 20, 2122, 33

Conservation of energyand momentum 256

Conservation of momentum 21, 22

Conservation of parity 227

Constructive and destructive interference 197

Contact angle (CA) 239

Contact resistance 153, 154

Contrast medium 258

Convection 145, 160

Conversion electron 230

Conversion of heat 148

Convex lens 51, 90

Cooling capacity 160

Coplanar forces 14

Cornu’s spiral 82

Corpuscle 229

Cosmic radiation 219

Coulomb field 172, 221

Coulomb forces 221

Coulomb potential 172

Coulomb’s law 170, 171

Coulometry 164

Counter tube 218, 225

Counting rate 216, 217, 210

Couple 14

Coupled oscillating circuits 194

Coupled Pendula 40, 41

Creeping 43, 44

Critical or optimum coupling 194

Critical point 57, 133

Cryoscopic constants 142

Cryoscopy 142

Crystal classes 255

Crystal lattices 254, 255260, 261, 262

Crystal structures 241, 242, 243249, 253, 254

255, 263

Crystal structures cubic 254

Crystal structures hexagonal 254

Crystal systems 254, 255260, 261, 262

Current balance 158

Current density 179

Curvature 13

Cycle 146

DDamped oscillation 184

Damped/undampedfree oscillation 43, 44

Index



Duration of oscillation 36

Dynamic and kinematicviscosity 56

Dynamic pressure 60

Ee/m 204

Earth’s magnetic field 174

Ebullioscopic constants 141

Edge diffraction 100

Efficiency 145, 148, 159, 161

Efficiency rating 160

Elastic after-effect 17

Elastic collision 21

Elastic hysteresis 17

Elastic loss 21, 22

Elasticity 16

Electric charge 172

Electric constant 170, 173

Electric discharge 115

Electric field 166, 169170, 172, 203

Electric field constant 89

Electric field strenght 170, 171

Electric flow 172

Electric flux 170

Electric theory of light 111

Electrical conductivity 144

Electrical eddy field 183

Electrical fields 166

Electrode polarisation 163, 165

Electrolysis 163, 164, 165

Electromagnetic fieldinteraction 112

Electromagnetic theoryof light 110

Electromagnetism 112

Electromotive force (e.m.f.) 156

Electron absorption 225

Electron avalanches 239, 240

Electron capture 226

Electron charge 203, 204

Electron collision 205, 206

Electron concentrationin gases 224

Electron diffraction 215

Electron in crossed fields 204

Electron mass 204

Electron oscillation 112

Electron spin 212, 213

Electron spin resonance 214

Electrons 236

Electro-optical modulator 113

Electrostatic induction 169, 170, 171

Electrostatic potential 170, 171172

Elementary charge 203

Energy-band diagram 161, 162

Energy ceiling 145

Energy detector 264

Energy dose 257

Energy level diagram(decay diagram) 222

Energy levels 209, 210, 211, 241242, 243, 244, 245246, 247, 248, 249250, 253, 263, 264

Energy loss 224

Energy of rotation 33

Energy of translation 33

Energy quantum 205, 206, 214

Energy term symbols 247, 248

Eötvös equation 57

Equation of adiabatic changeof slate 134

Equation of state 59, 128, 133

Equation of state forideal gases 130, 131

Equilibrium 14, 54

Equilibrium spacing 127

Equipotential lines 166

Equivalent dose and ion doseand their rates 257

Equivalent of heat 138

ESR 214

Evaporation 53

Exchange energy 209, 211

Excitation energy 205, 206209, 211

Excited nuclear states 222

Exitation of molecularvibration 115

Expected value of pulse rate 218

Exponential function 167, 168

Extension and compression 18

External photoelectriceffect 207, 208

Extrinsic conduction 235, 237238

Extrinsic conductivity 233, 234

FFabry Perot Etalon 117

Fabry-Perot interferometer 212

Falling ball viscometer 56

Faraday effect 112

Faraday’s contant 164

Faraday’s law 163, 164

Fermi characteristicenergy level 161

Ferromagnetic hysteresis 180

Ferromagnetic material 181

Fibre optics 120

Field intensity 172

Field strength 179

Filter 122, 181, 190

Fine structure 209, 222, 247, 248

First and second lawof thermodynamics 148

First law ofthermodynamics 130, 131, 138

Flammersfeld oscillator 134

Flat coils 176

Fluidity 56

Focal length 90

Focal point 197

Forbidden band 237, 238

Forbidden transition 209, 211227

Forbidden zone 233, 234, 235

Force 19

Forced cooling 160

Forced oscillation 43, 44

Fourier analysis 44

Fourier optics 121, 122

Fourier transform 121, 122

Four-point measurement 144

Four-wire method ofmeasurement 153

Franck-Hertz experimentwith Hg-tube 205

Franck-Hertz experimentwith Ne-tube 206

Fraunhofer diffraction 74, 75, 7677, 82, 97, 100

101, 102, 103, 104121, 122, 196

Free and fixed end 49

Free charges 173

Free fall 23, 24

Free path 157

Free path length 240

Free, damped, forced andtorsional oscillations 25

Freezing point depression 142

Frequency 49, 65, 6669, 70, 71, 89

Frequency doubling 119

Fresnel diffraction 74, 75, 76, 7782, 95, 97, 101

102, 103, 104

Fresnel biprism 92

Fresnel integrals 82, 100

Fresnel lenses 77

Fresnel mirror 92

Fresnel’s equations 110

Fresnel’s zone construction 76, 7795, 101

Fresnel zones 82, 196

Frictional resistance 60

Frustrated total reflection 199

Full-wave rectifier 188

G�-absorption 228, 234

�-emission 222

�-quanta 227, 229

�-radiation 230, 231

� rays 227

�-spectrometry 232

�-spectroscopy 228

g-factor 213, 214

G-modulus 47

Galvanic elements 163

Gas 132

Gas constant 59

Gas discharge tube 117

Gas laws 148

Gaussian beam 120

Index



Index

Gaussian distribution 218

Gaussian rule 172

Gay-Lussac theory 135

Gay-Lussac’s law 128, 149

Geiger-Nuttal law 130, 223

General equationof state for ideal gases 128, 164

Germanium 237, 238

Gibbs-Helmholtzequation 141, 142

Glass jacket system 142

Glow discharge 239, 240

Grade resistance 84

Gradient 172

Graetz rectifier 188

Graphite structure 215

Grating spectroscope 91

Gravitational acceleration 23

Gravitational constant 25

Gravitational force 39

Gravity pendulum 40, 41

Greenhouse effect 145

Grids 102

Group velocity 50

Grüneisen equation 127

Gyroscope 33, 34, 35

HH2O anomaly 53

Half life 167, 168, 216, 217

Half-life andradioactive equilibrium 216, 217

Half-shade principle 109

Half-value thickness 227, 251

Half-wave rectifier 188

Hall coefficient 233, 234

Hall effect 112, 175, 176, 233234, 235, 236

Hall mobility 236

Harmonic oscillation 36, 38, 39, 42

Harmonic sound intervals 61

Harmonic wave 50

Heat capacity of gases 130, 131

Heat capacity of metals 136, 137

Heat conductivity 147, 160

Heat insulation 147

Heat of vaporization 139, 140

Heat pipe 160

Heat pump 146, 160

Heat radiation 145

Heat transfer 147

Heat transition 147

Heat transport 144

Heating capacity 160

Heisenberg’s uncertaintyprinciple 99

Helium Neon Laser 117

Helmholtz arrangement 176

Helmholtz coils 174, 177

Helmholtz resonators 67

Henry’s law 141

High- and low-pass filters 116

High-pass filter 116, 181, 190

Holograms 114

Hooke’s law 15, 16, 17, 18

Hooke’s law oscillations 42

Horn antenna 198

Hothouse effect 147

Huygens’ principle 52, 74, 75, 7677, 78, 82, 101, 102

103, 104, 121, 122, 196

Huygens-Fresnel principle 68, 95

Hydrogen bond 53

Hysteresis 180

IIdeal gas 128, 133

Identity of atomic numberand charge on the nucleus 221

Illuminance 105, 106, 107

Image charge 170, 172

Impact parameter 221

Impedance 191, 192

Impurity depletion 237, 238

Inclinometer 174

Index of refraction 121, 122

Induced emission 115, 118, 119

Induced resistance 60

Induced voltage 183

Inductance 185, 187, 190

Inductance of solenoids 184

Induction 172, 175, 178179, 180, 182, 183

Induction constant 172

Induction impulse 193

Inductive and capacitivereactance 191

Inelastic collision 27

Inside diameter thickness 13

Instantaneous velocity 33

Integrating network 181

Intensity of characteristicX-rays 244

Intensity 100

Interaction potential 133

Interaction with material 231

Interface 57

Interference 52, 66, 68, 74, 75, 7677, 78, 79, 81, 82, 92

94, 95, 96, 97, 98, 101102, 103,104, 114, 116

181, 195, 241, 242, 243246, 249, 263

Interference in thin films 93

Interference ofelectromagnetic waves 212

Interference of acoustic waves 68

Interference of equal inclination 94

Interference of microwaves 195

Interference of thin layers 94

Interference of ultrasonic waves 79

Interferometer 81, 96, 97, 98, 181

Internal energy 136, 137

Internal conversionin 146mBa 230

Internal friction 55

Internal resistance 156, 161, 188

Intrinsic conduction 235, 237238

Intrinsic conductivity 233, 234

Intrinsic energy 135

Inverse Joule-Thomson effect 135

Inversion 115, 117, 118, 119

Inversion temperature 135

Ionizing particles 219

Ionizing energy 257

Isobars 130, 131

Isochoric and isothermalchanges 148

Isochors and adiabaticchanges of slate 130, 131

Isoclinic lines 174

Isogenic lines 174

Isomeric nuclei 230

Isotherms 130, 131

Isotopic properties 130, 223

Isotopic spin quantum numbers 230

JJoule effect 160

Joule-Thomson effect 135

KK� doublet splittingof iron X-rays 248

K� doublet splittingof molybdenum X-rays 247

Kerr effect 113

Kinetic energy 84

Kinetic theory of gases 132

Kirchhoff’s diffraction formula 99

Kirchhoff’s laws 155, 156, 185186, 190, 191

Klein-Nishina formula 229

Kundt’s tube 65

LL-Transition 263

Lambert’s law 107

Laminar flow 60

Landé factor 214

Laser 101, 102, 103, 104116, 117, 118, 119, 120

Laser Doppler anemometry 116

Laser physics 123

Lattice constant 241, 242243, 249, 263

Lattice planes 215

Lattice potential 127

Lattice vibration 136, 137


Laue method 255

Law of absorption 73, 251258, 259

Law of collision 21, 22

Law of distance 171, 198

Law of inductance 184

Law of induction 193

Law of gravitation 25

Law of lenses 90

Law of refraction 110

Laws of falling bodies 23, 24

Length 13

Lenses 121, 122

Lenz’s law 184

Lever 14

Lift and drag 60

Light intensity 107

Light quantity 107

Light velocity 98

Limit of elasticity 17, 18, 42

Linearity 197

Linear expansion 127

Linear motion 20, 2122, 84

Linear motion due toconstant acceleration 23, 24

Linear relationship betweenthe propagation time of soundand its respective path 62

Liquid 56

Littrow prism 117

Lloyd mirror 79

Loaded transformer 182

Local ion dose rate 257

Logarithmic decrement 43, 44

Longitudinal waves 62, 65, 7072, 73, 74, 7576, 77, 78, 7980, 81, 82, 83

Lorentz force 158, 204, 219233, 234, 235

Lorenz number 144

Lorentz-polarization factor 261262

Loudness 66

Loss resistance 187

Low-pass filter 181, 190

Low resistance 153

Luminance 105, 106, 107

Luminous flux 105, 106, 107

Luminous intensity 105, 106

Lyman-, Paschen-, Brackett-and Pfund-Series 210

MMagnet Board Mechanics 1 85

Magnet Board Mechanics 2 86

Magnet Board Optics 124

Magnetic Board Electricity 200

Magnetic Board Heat 149

Magnetic field 174, 175, 176177, 178, 179

Magnetic field constant 89

Magnetic field of coils 180, 183

Magnetic field of paired coils 176

Magnetic field of single coils 175

Magnetic field strength 180

Magnetic flow density 174

Magnetic flux 177, 178, 179182, 183, 193

Magnetic flux, coil 180

Magnetic flux density 175

Magnetic inclination anddeclination 174

Magnetic induction 183

Magnetic induction (formerlymagnetic-flux density) 158

Magnetic moment 177, 213

Magnetic resistance 233, 234235

Magnetostriction 181

Magnification 90, 97

Malus’ law 111

Mass absorptioncoefficient 251, 258, 259

Mass coverage 225

Mass-spring system 61

Material waves 215

Mathematical pendulum 36, 38, 39

Mathies rule 157

Maxwell disk 33

Maxwell relationship 91

Maxwell’s equations 173, 176, 178179, 183, 185

186, 193

Maxwell’s wheel 33

Maxwellian velocitydistribution 132, 213

Mean energy loss of�-particles per collision 224

Mean free path length 224

Mean ionization energyof gas atoms 224

Mean lifetime of ametastable state 118

Measurement accuracy 99

Measurement of projectilevelocities 27

Mechanical equivalent of heat 138

Mechanical hysteresis 16

Mechanical work 138

Medical 258

Medical application of X-rays 258

Melting 53

Mesons 219

Metallic film resistor 157

Metals (Hall effect) 236

Metastable states 211, 230

Mica plate 94

Michelson interferometer 81, 9697, 98

181, 195

Microscope 90

Microwaves 195, 196197, 198, 199

Miller indices 253, 254, 255260, 261, 262

Millikan experiment 203

Mirror 51

Mixture temperature 136, 137

Mobility 233, 234

Model kinetic energy 132

Modulation 89

Modulation of light 113

Modulus of elasticity 15, 47

Mohr balance 53

Mole volumes 130, 131

Molecular vibration 115

Molecule radius 133

Molecules 132

Moment 14, 28, 29, 30

Moment of inertia 27, 28, 29, 3033, 34, 35, 3738, 45, 46, 47

48

Moment of inertia of2 point masses 48

Moment of inertia of a bar 28, 48

Moment of inertia of acylinder 48

Moment of inertia of adisc 28, 48

Moment of inertia of amass point 28

Moment of inertia of a sphere 48

Moment of inertia of spheresand rods 25

Momentum 84

Monochromatization 245, 246 of X-rays 260, 261

262

Monomode and multimodefibre 120

Moseley’s law 232, 250252

Motion involving uniformacceleration 26

Motion track 19, 20, 21, 22

Moving charges 158

Multiple slit 75, 102

Multiplicity 209, 211

Multiplicity factor 261, 262

Multipole radiation 230

Nn-germanium (Hall effect) 235

Natural frequency 49

Natural vibrations 61, 64, 65

Nd-YAG laser 119

Neutrino 226

Newton’s law 30, 84

Newton’s 2nd law 19, 20

Newton’s ring apparatus 93

Newton’s rings 93

Newtonian andnon-Newtonian liquid 55

Newtonian liquid 56

Neyer-Neldel rule 235

No-load operation 156

Normal Hall effect 236

NTC 157

Nuclear transitions 230

Numerical aperture 120

Nutation 34, 35


Index



Index

OObject beam 114

Object distance 90

Ohm’s law 153, 154, 156, 165

Ohmic resistance 191

One-electron spectra 209

Operating point 162

Optic axis 108

Optical activity 109

Optical anisotropy 113

Optical instruments 90

Optical path difference 94

Optical pumping 118, 119

Optical resonator 115, 119

Optical rotatory power 109

Order of diffraction 241, 242243, 263

Ordinary andextraordinary ray 108

Orthohelium 209, 211

Oscillating circuits 194

Oscillation period 38, 39

Oscillations 38, 39, 42, 43, 44

Oscillatory circuit 184

Pp-germanium (Hall effect) 233, 234

p-n junction 161, 162

Pair formation 227, 231

Pair production 228, 251

Paraboloid of rotation 54

Parahelium 209, 211

Parallel conductance 194

Parallel springs 42

Parallel-T filters 181

Parallel-tuned circuit 187

Parent substance 216, 217

Particle energy 130, 223

Particle velocity 219

Paschen curve 240

Path difference 93

Path of a ray 90

Pauli method 194

Peltier coefficient 159, 160

Peltier effect 160

Peltier heat pump 160

PEM fuel cell 163

Pendulum oscillations 38, 39

Pendulum 37, 37, 38, 3940, 41, 43, 44

Period 36

Periodic motion 49

Phase 89, 92, 96, 98, 181

Phase and group velocity 70, 80

Phase center 198

Phase displacement 185, 186187, 190

Phase holograms 114

Phase relationship 93

Phase shift 66, 192

Phase velocity 49, 50, 199

Phasor diagram 192

Photo-conductive effect 161

Photo effect 228

Photoelectric effect 207, 208, 227 231, 251, 232

Photometric law 105, 106

Photon energy 207, 208

Photonuclear cross-section 231

Photonuclear reaction 230

Physical pendulum 37, 38, 39

Piezoelectric effect 70, 71

Piezoelectric ultrasonictransducer 71

Piezoelectric ultrasonicstransformer 70

Pin hole 76

Pin hole diaphragms 101

Planck’s constant 210

Planck’s “quantumof action” 207, 208, 249

Plane of polarisation 108

Plane parallel plate 94

Plastic flow 16

Plasticity 16, 55

Plasma Physics 239, 240

Plate capacitor 166

PLZT-element 113

Pohl’s pendulum 43, 44

Pohl’s plate 94

Poisson’s distribution 218

Poisson’s ratio 15

Poisson’s spot 76, 101, 104

Polar diagram 60

Polarimetry 109

Polariser 108

Polarizability 91

Polarization 108, 110, 111112, 115, 119

Polarization level 110

Polarization of light 113

Polarization of microwaves 197

Polarizer 111

Polarizer and analyzer 197

Polytropic equation 134

Positron 226

Potential 166, 169

Potential and kinetic energy 27, 84

Potential difference 172

Potential energy 33

Potential well model ofthe atomic nucleus 130, 223

Power and Work 154

Power matching 156

Precession 34, 35

Pressure 59, 140

Pressure and temperature 128

Principle of conservationof momentum 27

Prism 91

Projectile motion 26

Propagation of a wave 49

Propagation of soundwaves 63, 73, 83

PTC 157

Pull-out method 58

QQ factor 184, 187, 194, 257

Quantisation of energy levels 212

Quantity of light 105, 106

Quantum leap 206

Quantum number 214

Quarterwave plates 108

Quincke tube 66

Rr.m.s. value 188

Radiation 143

Radiation field 198

Radioactive decay 218, 219225, 228

Radioactive equilibrium 130, 216217, 223

Radioactive particles 219

Radioactive radiation 227

Range dispersion 224

Raoult’s law 141, 142

Rate of decay 216, 217

Ratio of attenuation/decrement 43, 44

RC filters 181

Reaction rate 109

Real and virtual image 114

Real charges 173

Real gas 133, 135

Real image 90

Reciprocal lattice 253, 254, 255260, 261, 262

Reconstruction 122

Recovering time and resolutiontime of a counter tube 218

Rectifier circuits 188

Reduced length of pendulum 37

Reference beam 114

Reflection 51, 68, 79, 81, 94110, 195, 199

Reflection coefficient 110

Reflection factor 110

Reflection of longitudinalwaves 72

Refraction 51, 94, 199

Refractive index 89, 91, 96, 98

Refrigerator 146

Relativistic Lorentz equation 226

Relaxation 16, 118, 119

Remanence 180

Resistance 153, 155, 187, 190, 192

Resistance to flow 60

Resistance to pressure 60

Resistivity 153, 154

Resolution of opticalinstruments 101


Resonance 184, 194, 214

Resonance frequency 43, 44, 67

Resonator cavity 117

Resonator modes 119

Rest energy 256

Resting energy 226

Restrictor valve 146

Reversible cycles 148

Reversible pendulum 37

Reynolds number 60

Rigid body 45, 46, 48

Ring method 57

Ripple tank 51, 52

Ripple voltage 188

RLC circuit 187

RLC measuring bridge 191

Rope wave 50

Rotary viscometer 55

Rotary motion 28, 31, 32, 54

Rotating liquids 54

Rotation 29, 30

Rotation niveau 115

Rotational energy 27, 29

Rowland grating 91

Rüchardt’s experiment 134

Rules governing selection 230

Rutherford atomic model 221

Rutherford experiment 221

Rydberg constant 210, 252

Rydberg frequency 250

Rydberg series 211

SSaccharimetry 109

Sampling theorem 116

Scattering 221 ,229

Scattering of light by smallparticles (Mie scattering) 116

Scintillation detectors 230, 231

Screening constant 252

Second order conductors 165

Seebeck coefficient 159, 160

Seebeck effect (thermoelectric effect) 159

Selection rules 209, 211, 247248, 264

Self-inductance 184, 192

Semiconductor 130, 161, 162223, 233, 234235, 237, 238

Semiconductor thermogenerator 159

Serial springs 42

Series connection 155

Series-tuned circuit 187

Shear modulus 25, 47

Shear stress 55

Shell structure of electronshells 232

Short circuit 156

Single electron atom 210

Single slit 74

Singlet and triplet series 209, 211

Slit diffraction 100

Slit 99, 103, 104

Slope efficiency 120

Smoothing factor 188

Solar cell 161

Solar ray collector 145

Solenoids 184

Sonar principle 80

Sound 62, 6569, 71

Sound pressure 69, 80

Sound velocity 69

Sound velocity in gasesand solids 65

Spatial and time coherence 97

Specific charge of the electron 204

Specific heat 144

Specific rotation 109

Specific thermal capacity 138

Spectra 209

Spectral lines(shape and half width value) 97

Spectral power density 116

Spectrometer-goniometer 91

Spectroscope 91

Spectroscopy with the X-ray energy detector 264

Spectrum of emission 115

Speed of light 181

Spin 209, 211

Spinorbit interaction 211

Spin-orbital angularmomentum interaction 209

Spin-orbit coupling 181

Spiral spring 40, 41

Spontaneous and stimulatedlight emission 117

Spontaneous emission 115, 118119

Spring constant 17, 18, 4041, 42, 45

46, 48

Square wave 181

Standard deviation 218

Standing waves 49, 64, 195

Statics 14

Stationary longitudinal waves 72

Stationary waves 64, 6568, 69

Stefan-Boltzmann’s law 143

Steiner’s law 37

Steiner’s theorem 25, 45, 46

Step response 181

Stereographic projection 259

Stern-Gerlach experiment 213

Stirling engine 148

Stokes’ law 56, 203

Straight conductor (magnetic field) 178

Stress 15

Structure amplitude 254, 255

Structure factor 253, 260261, 262

Structure of NaCl 253

Superimpositionof magnetic fields 178

Superimpositionof sound waves 63, 83

Superposition of waves 72, 7981, 82

Surface adhesion 58

Surface charge density 170, 171172

Surface energy 57, 58239

Surface of rotating liquids 54

Surface tension 57, 58

Surface treatment 239

Surface waves 51, 199

Sweep 194

TTelescope 90

Temperature 59, 132, 140

Temperature amplitudeattenuation 147

Temperature dependence 71

Temperature dependenceof resistances 143

Temperature dependence of resistors and diodes 157

Temperature gradient 144

Term diagram 227

Terminal voltage 156

Terrestrial gravitationalacceleration 37

Testoring torque 44

The Bragg equation 241, 242, 243244, 247, 248249, 252, 255

256, 263

Thermal 144

Thermal capacity 127, 138, 147

Thermal capacity of gases 134

Thermal energy 138

Thermal equation of state 133

Thermal expansion 127

Thermal pump 148

Thermal radiation 147

Thermal tension coefficient 128

Thermoelectric e. m. f. 143159, 160

Thermogenerator 159

Thomson coefficient 159, 160

Thomson equations 159, 160

Threshold energy 120

Throttling 135

Time constant 167, 168

Time measurement 13

Torque 16, 29, 34, 3540, 41, 44, 47, 177

Torque and restoring torque 43

Torsion modulus 16, 47, 48

Torsion pendulum 43, 44

Torsional vibration 40, 41, 43, 4445, 46, 47, 48

Total reflection 120, 199

Trajectory parabola 26

Transfer function 189


Index



Index

Transformer 182, 184

Transistor 162

Transit time 120

Transition probability 222, 230

Transmission 195, 199256

Transverse and longitudinalmodes 120

Transverse and longitudinalresonator modes 117

Transverse and longitudinalwaves 66

Transverse wave 49, 197

Tunnel effect 130, 199, 223

Turbulence 116

Turbulent flow 60

Two-electron spectra 209

Two-electron systems: He, Hg 211

Two-wire field 213

UUltrasonic 69, 70, 71, 72, 73

74, 75, 76, 77, 7880, 81, 82, 83

Ultrasonic diffraction 82

Ultrasonic Doppler effect 83

Ultrasonic Michelson-Interferometer 81

Ultrasonic velocity 80

Ultrasonic waves 72, 79

Uncertainty of location 99

Uncertainty of momentum 99

Uniform acceleration 84

Uniform magnetic field 158, 177

Universal gas constant 128

Universal gas constant degreeof freedom 131

Universal gas constant 128, 130

Unloaded transformer 182

Use of an interface 42, 68

VValence band 161, 162, 233

234, 235, 237238

Van der Waals equation 133, 135

Van der Waals force 135

Van’t Hoff law 139

Van’t Hoff factor 142

Vaporisation enthalpy 146

Vaporization 140, 146

Vapour pressure 140, 146

Vapour pressure of water 139, 140

Variable g-pendulum 38, 39

Velocity 19, 20, 21, 22

Velocity distribution 132

Velocity gradient 55

Velocity of light 89, 96, 120

Velocity of sound 62, 6569,71

Velocity of sound in air 66

Velocity of soundin liquids 69, 70, 71

Velocity of ultrasonics 70

Verdet’s constant 112

Vernier 13

Vibration 47, 48

Vibration niveau 115

Vibration of strings 61

Virtual image 90

Virtual light source 92, 9698, 181

Viscometer 55, 56

Viscosity 55, 56203

Viscosity measurements 56

Viscosity of Newtonian and non-Newtonian liquids 55

Visible spectral range 210

Voltage 155, 166169

Voltage doubling 188

Voltage source 156

Voltage stabilisation 188

Volume 128, 140

Volume expansion 53

Volume expansion of liquids 127

WWave 49, 50, 68, 72

Wave equation 50

Wavelength 49, 50, 64, 65, 66, 6970, 71, 72, 89, 92, 96

98, 181, 195, 260261, 262

Wave-particle dualism 99

Wave phenomena 51

Weak interaction 227

Weber-Fechner law 66, 109

Weight 13

Weight resolution 13

Weiss molecular magneticfields 181

Wheatstone bridge 155, 191

Wiedmann-Franz law 144

Wien-Robinson bridge 189

Wire loop 175, 176

Work function 207, 208

XX-ray 232, 233, 234, 235

241, 242, 243, 244245, 246,247, 248249, 250, 251, 252253, 254, 255, 256257, 258, 259, 260261, 262, 263, 264

X-ray bremsstrahlung 252

X-ray dosimetry 257

X-ray energy detector 264

X-Ray Experiments, Handbook 265

X-ray fluorescence 232

X-ray radiation 258, 259

X-ray spectral analysis 232

X-ray tube 242, 243, 249

YYoung’s modulus 15

ZZ diode 157

Zeeman effect 212, 214

Zener effect 157

Zone construction 77

Zone plate 77, 95


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For the student system “Advanced Optics

and Laser Physics” a special brochure

is available in English.

Special brochures

Additionally there are special brochu-

res for our particularly successful

teaching systems TESS (available in

German, English, French and Spanish),

Cobra3 (available in German, English)

and Natural Sciences on the board

(available in German, English).

– catalogues, brochures and more…


Phywe Systeme GmbH & Co. KGRobert-Bosch-Breite 10

D-37079 GöttingenGermany

phone: ++49/551/604-0fax: ++49/551/604-115

[email protected]

We reserve ourselves all rights concerning errors, translation,

partial reproduction and photocopies.

08.07.08 Order No. 16505.32 4th edition


Katalog me pune laboratori

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Transcript of Katalog me pune laboratori