hwk3 - c 4 + ( p e ) 2 c 2 . (4) See if you can massage...

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Physics 31: Homework #3 Due Thursday, Feburary 7, 2008 Problem A: When we considered the classical analog of Compton scattering, we wrote the following conservations equations for the x and y components of momentum and for the energy: mv = mv ± cos φ + Mu ± cos θ (1) 0= mv sin φ Mu ± sin θ (2) 1 2 mv 2 = 1 2 mv ± 2 + 1 2 Mu ± 2 (3) (a) Compare Eqs. (1) and (2) with the corresponding equations in the text for Compton scattering [Eqs. (2.16) and (2.17)]. How do they di±er? (b) Write the relativistic energy conservation equation for Compton scattering, that is, the case of a photon (frequency ν ) incident on an electron (mass M )atrest .Youw i l l need Eq. 1.24 from page 76 of the text. Hint: If the mass of the electron is M ,andits momentum after the collision is p ± e , then its energy after the collision is E =
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Unformatted text preview: c 4 + ( p e ) 2 c 2 . (4) See if you can massage your energy equation to get Eq. (2.19) in the text. (Note that the text is a little sloppy about using the symbol p for several dierent things. In Eq. (2.19), p is the electron momentum after the collision, the same quantity denoted by p e here.) (c) (Optional) Solve Eqs. (1)(3) to verify the result presented in class, 1 E 1 E 4 1 cos Mv 2 . (5) You should nd the solution to an exact quadratic equation for v , and then look for simplications using results valid for m/M 1. Do the following problems in Beiser: Chapter 3: 2, 3, 8, 16, 37 [For problem 3, you must use the relativistic momentum, Eq. (3.2)]...
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