Radiation Laws

A2

Head of Experiment: Yvonne Unruh

The following experiment guide is NOT intended to be a step-by-step manual for the experiment but rather provides an overall introduction to the experiment and outlines the

important tasks that need to be performed in order to complete the experiment. Additional sources of documentation may need to be researched and consulted during the experiment as well as for the completion of the report. This additional documentation must be cited in

the references of the report.

RISK ASSESSMENT AND STANDARD OPERATING PROCEDURE

1. PERSON CARRYING OUT ASSESSMENT

Name Geoff Green Position Chf Lab Tech Date 18/09/08

2. DESCRIPTION OF ACTIVITY

A2 Radiation Laws and Planck's Constant

3. LOCATION

Campus SK Building Blackett Lab Room 406

4. HAZARD SUMMARY

Accessibility X

Mechanical

Manual Handling

X

Hazardous Substances

Electrical X

Other

Lone Working Permitted?

Yes No Permit-to-Work Required?

Yes No

5. PROCEDURE PRECAUTIONS

Use of 240v Mains Powered Equipment Isolate Socket using Mains Switch before unplugging or plugging in equipment

Accessibility All bags/coats to be kept out of aisles and walkways.

Darkened area All bags/coats to be kept out of aisles and walkways. Switch on main light when not working on experiment.

6. EMERGENCY ACTIONS

All present must be aware of the available escape routes and follow instructions in the event of an evacuation

Experiment A2:

RADIATION LAWS AND PLANCK'S CONSTANT

The following experiment guide is NOT intended to be a step-by-step manual for the experiment but

rather provides an overall introduction to the experiment and outlines the important tasks that need

to be performed in order to complete the experiment. Additional sources of documentation may need

to be researched and consulted during the experiment as well as for the completion of the report.

This additional documentation must be cited in the references of the report.

The objective of this experiment is to determine Planck's constant using a standard tungsten light

bulb and a photodetector. The underlying assumption is that the tungsten filament radiates similarly

to a blackbody, permitting the use of the radiation laws to calculate Planck's constant h.

The black body spectrum is temperature dependent; therefore by measuring how the emitted

radiation intensity varies with temperature it is possible to determine Planck’s constant.

The energy flux rate IB(v,T) is described by Plank’s law:

1

12),(

)/(2

3

KThvBec

hvTvI (1)

where T is the temperature of the emitting body (in this experiment the temperature of the filament

within the bulb), v is the frequency of the emitted radiation, h is Planck’s constant and K is

Boltzmann’s constant. This equation was originally derived for modelling a perfect absorbing cavity.

However, conveniently, it also describes the spectrum of emitted radiation from a body in thermal

equilibrium. The radiation emitted from a so-called grey body can be written as:

),(),( TvITvI Bv (2)

where v is additional parameter called emissivity.

In this experiment the source of radiation (a tungsten filament) can be modelled as a grey body with

v being very nearly equal to 0.5. However, as the method used yields relative readings, the

knowledge of the emissivity is not needed as long as it does not change with frequency within the

range of interest.

Another important law concerning blackbody radiation was discovered by Wilhelm Wien, and

Wien’s law states that there is an inverse relationship between the temperature of the body and the

most prominent wavelength of the radiation emitted. This is only valid for very high frequencies v,

thus, allowing the approximation of equation 1 (Wien’s approximation) given below.

)/(

2

32),( KThv

B ec

hvTvI (3)

This approximation can be used as the frequency of light used in this experiment from the tungsten

lamp is to the order of 1015

Hz maximum, due to tungsten melting above 3680K.

Other assumptions that need to be made are; that the detector used to measure the intensity of light

provides a perfectly linear output, and that the bandpass interference filters used to filter the emitted

radiation have a very narrow bandwidth (it is about 10nm). This allows the output of the detector,

filtered by these narrow band filters, to be expressed as corresponding to infinitesimally small

interval of frequencies so that integration over frequency is not required. Using these assumptions

the following can be derived:

CvvFKT

hv ),(loglog 0

0 (4)

Here Ө is the intensity measured from the detector output, v0 is the frequency of the radiation

transmitted by the filter. F(v0,Δv) takes into account the frequency variables and C is an arbitrary

constant. Therefore, using this equation it is possible to see how h can be calculated by plotting a

graph of logӨ vs. 1/T. The equation representing this graph will be:

TK

hv 1log 0 + constant (5)

Therefore the gradient of this graph will be equal to K

hv0 , allowing h to be calculated.

In order to do this the temperature of the filament must be known. This is very difficult to measure

directly and has to be done indirectly using a Wheatstone bridge or by making appropriate

measurements of the current through the filament and the resistive voltage drop on the filament. This

makes it possible to determine the resistance of the filament and from this to calculate the

corresponding temperature.

EXPERIMENT

The source of radiation is a commercial filament lamp, and the detector is a photodiode, which has a linear

response if properly used. Two detectors are available, with or without an amplifier, providing output current

or output voltage being proportional to the input light intensity.

You will be taking measurements of the intensity while varying the filament temperature (as determined

indirectly using the Wheatstone bridge or by voltage / current measurements) for different spectral bands in

the visible region. These are isolated with a set of five bandpass interference filters.

The Wheatstone Bridge

A Wheatstone bridge can be balanced by varying the relative values of the four resistors (Figure 1).

When it is balanced, there is no current flowing through ammeter A1 and the following relation holds:

3

241

R

RRR (6)

Therefore one can determine RT, for example, if the bridge is balanced and if the other resistances

are known. R2 is a one ohm resistor. You do not need to know the value of R2 exactly since it will

cancel out when you calculate the ratio RT / R293 (see Table 1 below) in order to find the temperature (R3

and R4 are resistance boxes. RT is the resistance of the bulb at temperature T.). Also note that instead of

ammeter it is possible (and in some cases it is better) to use a voltmeter, providing that it has sufficiently high

input impedance.

The resistance of tungsten increases nearly linearly with temperature, as shown in table 1. Relative

measurements of the resistance of the filament can be made with the Wheatstone bridge.

Resistance/temperature table

TR/K

RT / R293

TR/K

RT/R293 TR/K

RT/R293

800

3.46

1400

6.78

2000

10.33

900

4.00

1500

7.36

2100

10.93

1000

4.54

1600

7.93

2200

11.57

1100

5.08

1700

8.52

2300

12.19

1200

5.65

1800

9.12

2400

12.83

1300

6.22

1900

9.72

2500

13.47

Table 1: R293 is the resistance of the bulb at room temperature

Resistance of filament at room temperature

In order to calculate the temperature of the filament you will need to know the resistance of the bulb at

room temperature, R293. Measuring this involves passing a current through the bulb, which may result in

heating, thus increasing R293. Since your final result depends strongly on this value, you must be

careful to ensure that the filament is not heating up. You might want to verify this by inserting a

digital multimeter set to measure current into the circuit as suggested in Figure 1 and examining the

variation of resistance with current.

Measure R293, the resistance of the bulb at room temperature by balancing the bridge. R293 should be of the

order of ½ Ohm. In order to increase resolution you should therefore set R3 to the highest possible value

and vary R4.

Your final result, the value of h, depends on your measurement of R293 so pay particular attention to any

sources of error.

You can also use, instead of the Wheatstone bridge, an appropriately connected voltmeter and ammeter to

determine the resistance of the filament. Think carefully how they should be connected to provide accurate

measurements.

N.B. The multimeter is a sensitive detector. Be very careful not to pass currents through it greater than

the range it is set on. Always start at the highest range and decrease it step by step if you are unsure.

Optical setup

You are provided with the bulb and its shielding, lenses, a variable aperture (iris), a set of interference

filters and photodiode detectors. The photodiode detectors are Si diodes (THORLAB). One of them

operates to give output current proportional to intensity of incoming light. The second detector, in

addition, includes an amplifier so it outputs voltage signal proportional to the light intensity. You

should use both detectors and compare the results. Linearity of the response of the detectors needs

to be tested.

Detector response

Determine that the response of the detector is linear and check that it does not saturate at the highest

light intensities. To do this, investigate the variation of the output intensity with amount of incident

light. This can be done by measuring how the detector signal varies with the distance between the detector

and the light bulb, and checking that the dependence is as expected. Another way of controlling how

much light reaches the detector is by using the variable aperture provided. Think carefully about how

to set this up on your optical bench, and be sure to focus the light down onto the detector. Also, be

careful in not applying too high voltage to the bulb!

Main experiment

Take measurements of intensity over as wide a range of T as possible for each of the five filters, taking

care not to saturate the detector. It is best not to vary the aperture during the experiment (why?). If

you do though, be sure to scale your results accordingly. Measure RT for each lamp current and hence,

using your value of find TR from table 1 or a graph plotted there from.

However this is effectively the mean temperature of the filament, which is in fact hotter at the middle

than at the ends (you may satisfy yourselves of this by observing what happens to the cold filament

as you slowly increase the current through it). From Wien's approximation we know that IB is

proportional to eh/KT

, which indicates that the radiation predominantly comes from the hottest central

part. Therefore T is lower than the effective radiation temperature, leading to a systematically low

value of h. This can be accounted for using the temperature correction curve appended.

After the temperature correction you should be able to determine h from your data, using the appended

transmission spectra of the filters from which you can obtain the peak wavelength.

Compare your value with the accepted value of h. Is it the same? If not, discuss any likely reasons for a

disparity, such as sources of error.

Transmission Curves for Thorlabs Bandpass Interference filters

Equipment Hints.

1) Power Supply Caution.

The power supply can destroy the light bulb. Always turn a power supply controls to zero

before switching on. Always turn on connected instruments that are monitoring the power

supply voltage and currents on before the power supply.

The power supply has a current limit control with a voltage limit. If the voltage limit is

set to 12V then the current control can be used to vary the intensity of the bulb. To set the

voltage limit the small black push button has to be out. In this position the voltage limit

and current limit can be set without any current flowing in the circuit. Once pressed in the

button allows current to flow in a controlled manner. Any voltage between zero and the

voltage limit can be selected by the current control knob.

2) Light Bulb Caution.

The light bulbs are very bright when operated at their rated voltage. Over time this will

result in an evaporation of the filament on to the glass bulb envelope. When setting up the

optics keep the bulb voltage at the minimum of what is required to see the beams of light.

Ten volts for a 12V

(20W) bulb produces enough light to prove or disprove the optical setup without

changing the long term properties of the bulb. There is zero guarantee that a replacement

light bulb will be usable with the resistance calibration of the previous bulb. So exercise

caution to avoid repeating the experiment. Also the alignment of the filament with respect

to the previous optics will likely be different. Check the on axis alignment of the filament.

There may be an offset that can be compensated for by tilting the optical saddle or bulb

holder.

3) Multimeter Caution.

As mentioned before, turn on the multimeter before the power supply. The multimeter

has two input terminals to measure current apart from the common terminal. The 10A

input is suitable for measuring up to ten Amps. The light bulbs use up to 1.7 amps so this

is the only input to use if the bulb current is to be more than 200ma.

The other mA terminal will work up to a few 100mA before an internal fuse blows.

Blowing this fuse costs time. This input can be used when determining the room

temperature bulb resistance. Do not forget to change the input back to 10A when the

room temperature bulb measurements are complete.

4) Bulb Resistance.

The tungsten filament will heat up if current is passed through it. This will change the

resistance of the bulb. Measuring the resistance of the bulb is a guide to the temperature

of the filament. Attempting to measure the resistance at room temperature with a

multimeter will likely heat up the bulb and indicate a high resistance due to connection

lead resistances and a slightly warmer filament temperature. Some control of the bulb

current is required to see what the resistance would be as the current approaches zero and

self-heating of the filament is minimised.

A Wheatstone bridge can be used to measure an unknown resistance if three of the other

resistors are known. The relative resistance of the connecting wires in the sections of the

bridge need to be taken into account. The bridge does require time consuming manual

adjustment to achieve an accurate balance.

Alternatively a four Wire measurement technique can be used. The current to the bulb is

supplied by two wires and the voltage is sensed by another pair of wires at a point very

close to the bulb filament. The voltage drop of the current carrying wires is eliminated.

Crocodile/Alligator connections are to be avoided where possible.