Download Experiment A14:

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
Position
Geoff Green
2. DESCRIPTION OF ACTIVITY
Chf Lab Tech
Date
18/09/08
Blackett Lab
Room
406
A2 Radiation Laws and Planck's Constant
3. LOCATION
Campus
Building
SK
4. HAZARD SUMMARY
Accessibility
X
Mechanical
Manual
Handling
X
Hazardous
Substances
Electrical
X
Other
Lone Working
Permitted?
Yes
No
5. PROCEDURE
Use of 240v Mains Powered Equipment
Accessibility
Darkened area
Permit-toWork
Required?
Yes
No
PRECAUTIONS
Isolate Socket using Mains Switch before unplugging
or plugging in equipment
All bags/coats to be kept out of aisles and walkways.
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:
2hv3
1
I B (v, T )  2 ( hv / KT )
c e
1
(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:
I (v, T )   v I B (v, T )
where  v is additional parameter called emissivity.
(2)
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.
I B (v, T ) 
2hv 3 ( hv / KT )
e
c2
(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:
log   
hv0
 log F (v0 , v)  C
KT
(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:
log   
hv0 1
+ constant
K T
Therefore the gradient of this graph will be equal to 
(5)
hv0
, allowing h to be calculated.
K
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:
R1 
R4R2
R3
Therefore one can determine
(6)
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
800
900
1000
1100
1200
1300
RT / R293
RT/R293
TR/K
TR/K
3.46
1400
6.78
2000
4.00
1500
7.36
2100
4.54
1600
7.93
2200
5.08
1700
8.52
2300
5.65
1800
9.12
2400
6.22
1900
9.72
2500
Table 1: R293 is the resistance of the bulb at room temperature
RT/R293
10.33
10.93
11.57
12.19
12.83
13.47
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.