HWsol11_oops2

HWsol11_oops2 - Physics 2214 Fall 2008 Solutions to Problem...

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Unformatted text preview: Physics 2214 Fall 2008 Solutions to Problem Set #11- 1 - K. Selby 11/25/08 1 . Compton Scattering (a) The scattered photon has 2/3 of that of the incident photon. Then hc λ′ = 2 3 ⎝ ⎜ ⎛ ⎠ ⎟ ⎞ hc λ and λ′ = 3 λ 2 The relationship between the wavelengths of the incident and scattered photons is λ′- λ = h m e c (1 - cos θ ). Then 3 λ 2- λ = h m e c (1 - cos 90° ). Solving for λ gives λ = 2h m e c = 2(2.43 pm) = 4.86 pm . The incident photon is shown on the left, with the emitted photon and the recoiling electron to the right. (b) Let the momenta of the incident and scattered photon be p → and p → ′ , respectively. Let the momentum of the recoiling electron be p → e . Then conservation of momentum gives p → ′ + p → e = p → Take components in the x- direction (see diagram above): p e cos α = p (1) Take components in the y- direction: p e sin α = p ′ . (2) Square and add Eqs. (1) and (2), then take the square root: p e = p 2 + p ′ 2 = (h/ λ ) 2 + (h/ λ′ ) 2 = ⎝ ⎜ ⎛ ⎠ ⎟ ⎞ h λ (1) 2 + (2/3 ) 2 = 13h 3 λ . - 2 - Now let's put in the numbers:...
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This note was uploaded on 12/24/2008 for the course PHYS 2214 taught by Professor Giambattista,a during the Fall '07 term at Cornell.

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HWsol11_oops2 - Physics 2214 Fall 2008 Solutions to Problem...

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