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1137_Physics ProblemsTechnical Physics

1137_Physics ProblemsTechnical Physics - 478 P40.38...

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478 Introduction to Quantum Physics P40.38 From the condition for Bragg reflection, md d λθ φ == F H G I K J 22 2 sin cos . But da = F H G I K J sin 2 where a is the lattice spacing. Thus, with m = 1, λ φφ = F H G I K J F H G I K J = 2 aa sin cos sin FIG. P40.38 h p h mK e 2 = ×⋅ ×× × −− 6626 10 10 54 0 1 60 10 167 10 34 31 19 10 . .. . Js 2 9.11 kg J m ej e j . Therefore, the lattice spacing is a × ° = sin . sin . 50 0 218 10 0218 10 10 m nm . P40.39 (a) Ep cm c 2 2 4 =+ with Eh f = , p h = and mc h = C so hf hc 2 λλ C 2 and f c F H G I K J 2 2 11 C 2 (Eq. 1). (b) For a photon f c = 1 . The third term 1 C in Equation 1 for electrons and other massive particles shows that they will always have a different frequency from photons of the same wavelength . *P40.40 For the massive particle, Km c =− γ 1 2 bg and m h p h mv . For the photon (which we represent as ), EK = and == = = c f ch E ch K ch mc 1 2 . Then the ratio is m ch mv mc h v c =
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