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1143_Physics ProblemsTechnical Physics

1143_Physics ProblemsTechnical Physics - 484 P40.58...

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484 Introduction to Quantum Physics P40.58 Isolate the terms involving φ in Equations 40.13 and 40.14. Square and add to eliminate φ . h m v e 2 0 2 2 0 2 2 2 1 1 2 λ λ θ λ λ γ + L N M O Q P = cos Solve for v c b b c 2 2 2 = + e j : b h m e = + L N M O Q P 2 2 0 2 2 0 1 1 2 λ λ θ λ λ cos . Substitute into Eq. 40.12: 1 1 1 1 0 2 1 2 2 2 + F H G I K J L N M O Q P = = + F H G I K J = + h m c b b c c b c e λ λ γ . Square each side: c hc m h m c h m e e e 2 0 2 2 0 2 2 2 2 0 2 2 0 2 1 1 1 1 1 1 2 + L N M O Q P + L N M O Q P = + F H G I K J + L N M O Q P λ λ λ λ λ λ θ λ λ cos . From this we get Eq. 40.11: ′ − = F H G I K J λ λ θ 0 1 h m c e cos . P40.59 Show that if all of the energy of a photon is transmitted to an electron, momentum will not be conserved. Energy: hc hc K m c e e λ λ γ 0 2 1 = + = b g if hc = λ 0 (1) Momentum: h h m v m v e e λ λ γ γ 0 = + = if ′ = ∞ λ (2) From (1), γ λ = + h m c e 0 1 (3) v c m c h m c e e = + F H G I K J 1 0 0 2 λ λ (4) Substitute (3) and (4) into (2) and show the inconsistency: h h m c m c m c h m c m c h h h m c h m c h h m c h e e e e e e e e λ λ λ λ λ λ λ λ λ λ 0 0 0 0 2 0 0 0 0 2 0 0 1 1 2 2 = + F H G I K J + F H G I K J = + + + =
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