29:30 Physics IV Experiment 6

Experiment 6 : The Compton Effect

Purpose:

To observe the Compton shift in the energy of photons scattered by free electrons.

Discussion:

When a quantum of electromagnetic energy (a photon) is scattered by an electron, the electron recoils, thereby taking away some of the energy and reducing the energy of the photon. The energy of the photon is E = hf = hc/

and its momentum is p = E/c = h/

. Then using only conservation of energy and momentum, one easily derives the Compton formula:

' = + (h/mc)(1 - cos )

1/E' = 1/E + (1/mc²)(1 - cos )

where the primes denote after the scattering and m is the electron mass.

Procedure:

In this experiment a very intense source of Cs-137 is used to provide 662 keV photons. Extreme caution should be used to insure that you are not exposed to the direct radiation from this source for any extended period of time. Let the instructor remove the source from its container and insert it into its collimating shield. Monitor the radiation level in your vicinity periodically to be sure it's at a safe level.

The scattered photons will be detected by a NaI(Tl) scintillation counter (review Experiment 4) and stored in a Multi-Channel Analyzer (review Experiment 5). Before beginning, the MCA must be calibrated. Take a spectrum using a weak Cs-137 source. Determine the channel number corresponding to the photopeak in this spectrum. Repeat using a Ba-133 source. In this spectrum the two strongest lines are at 82 keV and 356 keV. Plot the observed channel numbers versus the corresponding energies to obtain the (linear) relation between channel number and energy.

Now take spectra of the radiation scattered by an aluminum rod for several scattering angles using the strong source. Convert the channel numbers determined for the observed peaks to energies using your calibration curve. Care must be taken to use maximum collimation of the source and maximum shielding of the detector if the peaks are to be clean. At one or two of the angles use the subtract mode of the MCA to remove background, observed with the aluminum rod removed for the same length of time as the main run.

Report:

Compare your results with the predictions of Compton's formula. This may conveniently be done by plotting 1/E' versus (1 - cos

) which should give a straight line according to eq. 2. Find the slope of this line and use your result to find mc². Compare your answer with the accepted value of 511 keV. Discuss the departure of any of the points from the straight line.

Extra:

As an additional problem, derive an expression for the shifted energy using the classical expression for the electron's energy (E = p²/2m). Compare the predictions of this result with those of the Compton formula and with your experimental results. Do your results rule out the use of classical mechanics for explaining the Compton effect?