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by: Eleazar Batz


Eleazar Batz
GPA 3.72


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Class Notes
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This 5 page Class Notes was uploaded by Eleazar Batz on Wednesday September 30, 2015. The Class Notes belongs to PHYS 302 at Western Kentucky University taught by Staff in Fall. Since its upload, it has received 8 views. For similar materials see /class/216686/phys-302-western-kentucky-university in Physics 2 at Western Kentucky University.


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Date Created: 09/30/15
COMPTON EFFECT D L Humphrey Physics 302 The Compton effect or Compton scattering is the scattering of photons by free electrons Classical electromagnetic theory says that when an electromagnetic wave of frequency v is incident on free electrons the electrons absorb electromagnetic radiation and oscillate with frequency v The oscillating electrons in turn reradiate electromagnetic waves of the same frequency V This is referred to as coherent scattering ie there is no change in the wavelength The scattering of very short wavelength radiation is observed to disagree with this The scattered radiation is observed to consist of two frequencies the original frequency v or wavelength 7 and another frequency v lt v or wavelength A gt1 The correct explanation of the modi ed wavelength in xray scattering was given by A H Compton in 1922 He adopted the quantum hypothesis and by applying the laws of conservation of momentum and energy was able to calculate the change in frequency or wavelength of the radiation Illa Fig 1 Scallorlng Caused by Compton lnleraellon Figure 1 shows schematically the collision between the incident photon and a free electron assumed to be at rest The photon has energy hv and momentum hvc and the electron has rest mass energy of moc After the collision the scattered photon has an energy of hv lthv and momentum hvc lthvc The wavelength of the scattered photon X is larger than A The decrease in the energy of the photon namely hv hv appears as the kinetic energy KB of the recoil electron From relativity 2 2 2 1 he mc moc moc 1 where 3 We v being the velocity of the recoil electron The relativistic momentum of the electron pe is mOBc V1 32 Now suppose that that the scattered photon and the recoiling electron make angles 6 and 1 respectively with the direction of the incident photon as shown in Fig 1 Applying the conservation of momentum to the collision for the X and Y components yields pezmvm c h Vh V cosepecos I c c 0thsin9 pesin L1 The conservation of energy gives hv hv39 K5 3 The solution of the above set is found by rewriting the momentum equations as pee c054 hv hvl cos 6 K4quot pee sin hv hv sin 6 5 Squaring and adding these equations yields p38 hv2 hv 2 2hvhv cos a G The total energy Ea of the recoiling electron is E3 Ke moo2 11v hvl mocz 7 which from relativity is also equal to EeVpe39C m6e 3 Equating Eqs 7 and 8 and squaring yields pfc2 hv hv 2 2hv hv39m0cz m Again equating the values of pezc2 from Eqs 6 and 9 and then solving for hvl yields hv r 3 llV 7 l hvmoc39xl cos 9 By using the relation 7w Xv c we may write the change in wavelength A l 1 due to the Compton effect as t h Aii i 1 cosei Cquot moc Experimental Method The rst thing to do is to assemble the electronics as shown in the Fig 2 The NH shoult39 he a 2 inch diameter crystal It should have a lead shield around the crystal lead brick with a 2 inch hole The high voltage for the detector should be set at 1000 V The ampli er Gain should be chosen so that a C0 spectrum covers about 1000 channels Using a 5CS a 6 Co source and a lea source obtain a calibration curve for the multichannel analyzer Have the lab instructor place the container with the 150 millicurie NCS source on the table in the proper position as shown in Fig 3 Place lead bricks so that the gammaray beam is collimated to the size of the aluminum scatterer Place other lead bricks so that the detector is shielded from the source by two to three bricks Acquire a spectrum at several angles and determine the energy of the photopeak of the Compton scattered photon using your calibration curve MCA TOP VEW scAltEnINu SAMPLE sosd y39nEvEevon Compton Scattering Experimental Method addendum The data acquisition system has already been calibrated for this experiment The PC displays the number of counts number of gamma rays entering the detector versus the energy in keV of the detected gamma ray or other event To utilize the data acquisition system you should familiarize yourself with the following operations of the system a Acquire data b Stop the acquisition of data c Acquire for a preset time 1 Change the vertical scale e Set up a region of interest I Print a graph of the display g Save a spectrum Part 1 Verify the correctness of the calibration by placing 60Co source in front of the detector There should be two peaks at l 172 keV and 1332 keV Remove the 60Co source and place the I37Cs source in front of the detector There should be a peak at 662 keV It may be necessary to correct the calibration by adding an offset Ask the instructor about this Pan 2 Have the lab instructor place the 150 millicurie 137Cs on the table in the proper position as shown in Figure 3 Acquire a spectrum at scattering angles of 20 to 90 in increments of lO and determine the energy of the photopeak of the Compton scattered photon Analysis Plot El calculated vs 6 on linear graph paper Put the experimental points with the estimated error on the curve Another analysis which gives 21 curve that is easily tted is obtained by wn39t39mg Eq 10 as Equot E quot 1 1936 E70 cos 6 and 1 151119561 Cose E I39 l 1 1 A plot of E vs 1 cos 9 should be a straight line With Intercept 131 and a slope Y equal to 1956 Make such a plot and do a least squares t to the data 1E


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