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1148_Physics ProblemsTechnical Physics

# 1148_Physics ProblemsTechnical Physics - Chapter 40 P40.70...

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Chapter 40 489 P40.70 Let u represent the final speed of the electron and let ′ = F H G I K J γ 1 2 2 1 2 u c . We must eliminate β and u from the three conservation equations: hc m c hc m c e e λ γ λ γ 0 2 2 + = + [1] h m u h m u e e λ γ λ θ γ β 0 + = cos cos [2] h m u e = λ θ γ β sin sin [3] Square Equations [2] and [3] and add: FIG. P40.70 h m u h h m u h h m u m u h h m u h m u h m u h m u u c e e e e e e e e 2 0 2 2 2 2 2 2 0 2 0 2 2 2 2 0 2 2 2 2 2 2 0 2 0 2 2 2 2 2 2 2 2 2 2 1 λ γ λ γ λ θ λ λ γ θ λ γ λ λ γ γ λ γ θ λ θ λ λ + + + = + + + = cos cos cos cos Call the left-hand side b . Then b bu c m u e = 2 2 2 2 and = + = + u b m b c c b m c b e e 2 2 2 2 2 2 . Now square Equation [1] and substitute to eliminate γ : h m c h h m c h h m c m c u c m c b e e e e e 2 0 2 2 2 2 2 2 0 2 0 2 2 2 2 2 2 2 2 2 1 λ γ λ γ λ λ λ γ λ + + + = = + .
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