Chapter3_21 - ) cos 1 ( 1 1 = c m p p p p e and ) cos 1 ( 1...

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PHY3063 R. D. Field Department of Physics Chapter3_21.doc University of Florida Compton Scattering (2) θ Photon: E 1 , p 1 Photon: E 0 , p 0 Before Electron at Rest Electron: E 2 , p 2 After Ψ Momentum Conservation Energy Conservation ψ θ sin sin cos cos 2 1 2 1 0 p p p p p = + = 1 2 0 2 2 1 2 0 E c m E E E E c m E e e + = + = + Thus, sin sin cos cos 2 1 2 1 0 p p p p p = = 2 2 2 1 2 0 2 2 2 1 2 0 2 2 ) ( ) ( ) ( ) ( c m E c m E cp E c m E E e e e + = + = and 2 2 1 0 2 2 2 2 2 2 1 2 1 0 ) ( ) ( sin ) cos ( c m p c m p p p p p p e e + = = + The first equation comes from squaring and summing the momentum conservation equations and the second equation comes from energy conservation. Thus, 2 2 1 0 2 2 1 2 1 0 ) ( ) ( sin ) cos ( c m p c m p p p p e e + = + , and after a little algebra we see that
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Unformatted text preview: ) cos 1 ( 1 1 = c m p p p p e and ) cos 1 ( 1 1 1 1 = c m p p e . If we now set p = h/ and p 1 = h/ 1 , we get ) cos 1 ( ) cos 1 ( 1 = = = c e c m h where nm m c m h e c 002427 . 10 427 . 2 12 = = = , and m c m e c 13 10 862 . 3 = = h D . Agrees with the data! Compton wavelength of an electron...
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