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 . hm v e 2 0 22 0 222 11 2 λλ θ γ + L N M O Q P = cos Solve for v c b bc 2 2 2 = + ej : b h m e =+ L N M O Q P 2 2 0 0 2 cos . Substitute into Eq. 40.12: 1 1 0 2 12 2 2 + F H G I K J L N M O Q P == − + F H G I K J = + h mc b cb c e . Square each side: c hc m h m c h m e ee 2 0 2 2 0 2 2 2 2 0 0 21 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 cos . From this we get Eq. 40.11: ′− = F H G I K J 0 1 h 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 Km c 0 2 1 = += bg if hc = λ 0 (1) Momentum: hh mv γγ 0 = if ′=∞ (2) From (1), h e 0 1 (3) vc c e e =− + F H G I K J 1 0 0 2 (4) Substitute (3) and (4) into (2) and show the inconsistency: c mc h c h c h e e e e e e e e 00 0 0 2 0 0 0 0 2 0 0 2 2 F H G I K J + F H G I K J = + + + = + . This is impossible, so all of the energy of a photon cannot be transmitted to an electron. P40.60 Begin with momentum expressions:
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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