BLACKBODY RADIATION
I.
Introduction:
The spectrum of light waves emitted from a hot, glowing object cannot be explained by the classical
theories of radiation and temperature, theories brought forward by Lord Rayleigh and by Jeans at the
end of the 19th century. Their “prediction” was that the intensity of the light emitted at a given
wavelength should vary inversely as the fourth power of the wavelength….which means that the
highest intensity occurs in the short wavelength or “ultraviolet” region. In fact, the predicted intensity
grows without bound as the wavelength goes to zero so all objects should appear to be blue no matter
what their temperature, and the total intensity of light emitted is infinite. Both these “predictions” are
incorrect and this state of affairs, called the Ultraviolet Catastrophe, persisted until Planck proposed the
idea that light waves are not continuous, but for some reason the light energy is emitted in small
“chunks” of energy called quanta (singular: quantum). Each quantum has energy E = hf, where h =
6.626x10-34 J·s is a fundamental constant of nature called Planck's constant. Introducing this idea,
Planck derived his distribution function, which has the property that the graph of intensity vs.
wavelength peaks at a wavelength that is inversely proportional to the absolute temperature of the
emitter (Wien Displacement Law), and that the total intensity of the light emitted per m2 of surface
area, integrated over all wavelengths, is proportional to the fourth power of the absolute temperature
(Stefan-Boltzmann Law).
An object, which absorbs all light incident on it is known as a Black Body. In this experiment we will
study the radiation emitted from a perfect black body and try to verify Planck's distribution formula. As
a perfect black body is just a theoretical object and cannot be made, we shall instead use a cavity. A
cavity is a hollow object with a small aperture, so any light that goes into it gets trapped and a little
light is emitted from the aperture, which is similar to the nature of black body radiation.
II.Required Equipment:
PASCO spectrophotometer, IR
sensor, Blackbody Light Source
with Light Aperture and Lens
assemblies, HP power supply,
Digital Multimeter (DMM),
Science Workshop interface
with Data Studio software.
III. Procedure:
The PASCO prism spectrophotometer used in this
experiment allows for the
measurement of the intensity of infrared radiation as a function of its wavelength. The source of the
radiation is a light bulb that is heated to a known temperature by adjusting the voltage V across its
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filament. The temperature can be calculated from the resistance of the filament at room temperature,
and the current through the bulb. The resistance of the bulb as a function of temperature is
approximately given by the equation:
R = R0 [1 + (T-T0)]
where,
is the thermal coefficient of resistance (4.5x10-3/°K for a tungsten filament),
T0 = 300K (room temperature),
R0 is the room-temperature resistance of the filament (measured to be 0.94 ohms).
From Ohm’s Law, R=V/I where I is the current through the filament. Substituting and solving for T,
we get the equation:
T = 300K + (4.5x10-3/K)-1 [V/(0.97 I) – 1]
The wavelength of the light is related to the angle at which it emerges from the prism. However, since
the index of refraction of the prism is a function of the wavelength of the light, the relationship
between wavelength and angle is somewhat complicated. In this experiment, the corresponding
equation has been determined for the spectrophotometer you are using.
A.
Determination of Intensity as a Function of Wavelength.
The light intensity as a function of angle will be measured using the Data Studio program, for four
different voltages across the bulb in the range from 5-9 V. The computer interface has been set up for
you, and an Intensity vs. Wavelength graph has been defined. The procedure to make a measurement
is as follows:
Open the Data Studio program and open “Black Body.ds” (File->) which you will find on the desktop.
The file should not have any data (Look into the left panel to see if there are any “Runs”). In case it has
any data, go to Experiment -> Delete ALL Data Runs. You are now ready to start the experiment.
Carefully rotate the “light sensor” arm on the spectrometer in a counter-clockwise direction until it hits
the stop on the angular indicator of the circular table. All four runs will start in this position. Set the
voltage across the light bulb, using the power supply and digital meter, to a value in the range from 59V, and record this value on your lab report form. Remove the magnet fixed in between the rotary
sensor and the spectrometer. Do this by pulling out the box holding the rotary sensor and taking out the
small square magnet. One person will start and stop the data run and view the resulting intensity vs.
wavelength plot, while a second person will “tare” the IR sensor and move the arm of the spectrometer
to scan the spectrum. Click on the green START button of Data Studio next to the timer at the top of
the screen. This will become the red STOP button, at which time the data taking can begin. Tare the
IR sensor by pushing its tare button (located on the top front of the sensor) while holding your hand in
front of the lens to prevent light from the bulb from reaching the sensor. This establishes the “zero
intensity” IR level. Next, uncover the lens and begin to rotate the arm of the spectrometer clockwise,
slowly and steadily. At first nothing may seem to be happening, but eventually the intensity level on
the Intensity vs. Wavelength plot will begin to rise and then fall as the wavelength (x-axis) increases.
Continue the scan until the indicated wavelength is 2500 nm, then press the STOP button of Data
Studio. This entire wavelength-scan process should take about one minute or so.
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Next, record the temperature of the bulb for this run on your lab report form. To do this, click on ADD
DISPLAY on the EXPERIMENT menu of Data Studio and select TABLE. Find “Temperature” on
the data parameters display on the left of the screen and drag the data for Run 1 (or the run you just
did) onto the Table. Two columns should appear: Time and Temperature. Click on the Temperature
column and then on the  button on the Table. This will give you the mean and standard deviation of
the measured temperature, calculated according to the equation given above. Next Click on the arrow
next to the  button and choose “Standard Deviation” and “Count” from the drop down menu. The
temperature should be in the range of a few thousand degrees. [If it is ten times that, then the scale on
the current sensor was set improperly. Ask your lab assistant for help in fixing this problem (you will
have to take another run after the correction is made.)] Record the mean temperature and standard
deviation on your lab form.
Repeat the above process for four different light-bulb currents. After changing the bulb current give the
bulb some time to come to a steady temperature. Make sure you close the temperature table before you
start each run otherwise it will drastically slow down the data acquisition process. Each lab partner
should make at least one scan.
After the runs are completed, go to the DATA button on the graph toolbar and deselect all the runs
except one (say Run1). Then click on the  button on the graph toolbar and you will see statistics being
displayed at the top of the graph. Click on the arrow next to the  button and check on “Area”,
“Standard Deviation” and “Count” and uncheck “min”. Make sure all the statistics are clearly visible
on the graph. Then take print outs for each of the member of the group. Now uncheck the current run
from the graph toolbar and select the next one from the list and repeat the above procedure. Print out
graphs for all the graphs for each member of the group. Finally, select all the runs from the graph menu
and then click on the  button to remove all the statistics from the graph. Now take a print out of this
graph with all the runs in it. This will help you in verifying Wien's Displacement Law. If all the
members of the group have graphs of all the runs done individually and one graph of all the run
together then you are done.
NOTE: At this point, data-taking is complete and the remainder of the analysis can be done
elsewhere. Before you leave the lab, all measurements must be complete and each lab partner must
have a complete data sheet initialed by your TA, including four measurements of the bulb temperature,
the wavelength at the maximum of the sensor-voltage plot, and the integral of the sensor voltage. Also,
each lab partner should have one plot initialed by the TA.
B.
Interpretation.
The data plots you made will look like the Planck distribution…going to zero quickly at short
wavelengths and less quickly at long wavelengths. The location of the peak of the distribution should
be rather well determined, and the integral from 500- 2500 nm should be a reasonably good (though not
entirely accurate) measure of the total output of the source. (1) Determine the constant in the Wien
Displacement Law by multiplying the wavelength at maximum IR output by the absolute temperature,
for all four runs (use the last graph that you printed, the one with all the curves, to do this). Find the
mean and standard deviation of these four measurements and compare with the standard value of
2.898x10-3 mK.
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To what degree of precision do these values agree? (2) Check the Stefan-Boltzmann Law by dividing
the integral of the sensor voltage readings from 500-2500 nm by the fourth power of the measured
temperature for each run (it is convenient to express the temperature in units of thousands of degrees K
to avoid small numbers). Determine the mean and standard deviation of the four measurements. To
what degree of accuracy do the data follow the Stefan-Boltzmann Law? (3) Discuss possible sources
of error in your measurements, and the way they might affect your results.
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