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1130_Physics ProblemsTechnical Physics

1130_Physics ProblemsTechnical Physics - Chapter 40 P40.25...

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Chapter 40 471 P40.25 (a) Conservation of momentum in the x direction gives: p p p e γ γ θ φ = + cos cos or since θ φ = , h p h e λ λ θ 0 = + F H G I K J cos . [1] Conservation of momentum in the y direction gives: 0 = p p e γ θ θ sin sin , which (neglecting the trivial solution θ = 0) gives: p p h e = ′ = γ λ . [2] Substituting [2] into [1] gives: h h λ λ θ 0 2 = cos , or ′ = λ λ θ 2 0 cos . [3] Then the Compton equation is ′ − = λ λ θ 0 1 h m c e cos a f giving 2 1 0 0 λ θ λ θ cos cos = h m c e a f or 2 1 1 1 0 2 cos cos θ λ θ = hc m c e a f . Since E hc γ λ = 0 , this may be written as: 2 1 1 2 cos cos θ θ γ = F H G I K J E m c e a f which reduces to: 2 1 2 2 + F H G I K J = + E m c E m c e e γ γ θ cos or cos . . . . θ γ γ = + + = + + = m c E m c E e e 2 2 2 0 511 0 880 0 880 0 732 MeV MeV 1.02 MeV MeV so that
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