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MidtermSolutionsFa07

MidtermSolutionsFa07 - Midterm Examination Physics 115A...

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Midterm Examination November 5, 2007 Physics 115A, Fall 2007 E. Abers Midterm Examination Solutions and Comments Name 1. 2. 3. 4. Total You may find some of the following useful: integraldisplay -∞ e - ax 2 dx = radicalbigg π a integraldisplay -∞ x 2 e - ax dx = 1 2 radicalbigg π a 3 integraldisplay 0 x n e - x dx = n !
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2 Midterm Examination Question 1 [20 Points] A photon with angular frequency ω strikes a free electron at rest. The electron absorbs the photon, and acquires some speed v . Is this process possible? If so, what is the speed of the final electron? If not, show mathematically why not? SOLUTION Suppose the final electron has momentum p and energy E = radicalbig p 2 c 2 + m 2 c 4 . The initial photon has energy planckover2pi1 ω and momentum q where | q | = planckover2pi1 ω/c . Energy conservation requires planckover2pi1 ω + mc 2 = E and momentum conservation requires q = p These are not independent! We also need E 2 = p 2 c 2 + m 2 c 4 Therefore pc + mc 2 = radicalbig p 2 c 2 + m 2 c 4 or p 2 c 2 + 2 mpc 3 + m 2 c 4 = p 2 c 2 + m 2 c 4 and q = p = 0, which is incorrect.
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