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 12 u c . We must eliminate β and u from the three conservation equations: hc mc hc ee λ 0 22 += +′ [1] h mu h θγ 0 +− =′ ′ cos cos [2] h e sin sin [3] Square Equations [2] and [3] and add: FIG. P40.70 h h hmu h hh h uc e e e e 2 0 2 222 2 2 0 2 0 2 0 2 2 2 0 2 0 2 2 2 2 1 θ λλ γθ ++ =′ + = cos cos cos cos Call the left-hand side b . Then b bu c e 2 2 and + = + u b mb c cb b 2 2 . Now square Equation [1] and substitute to eliminate : h h hmc h b e e e 2 0 2 2 2 2 0 2 0 2 2 2 1 = =+ . So we have h e 2 0 2 2 2 2 0 2 0 2 + + h 2 2 0 2 2 2 0 2 0 2 cos cos Multiply through by 0 e λλγ λγ γλ λλ γ γγ 0 2 0 2 0 0 0 2 2 0 2 2 0 2 2 2 2 2 1 2 1 2 1 2 1 ′+ −− = + + ′− F H G I K J + F H G I K J =− F H G I K J h h h u hu h u c h u c h u c h e e e e cos cos cos cos a f The first term is zero. Then
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