exam2_003 - Physics 3101, Introduction to Modern Physics,...

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Introduction to Modern Physics , Spring 2005 EXAM #2 Wednesday, March 30, 2005 Instructions Read each problem carefully before starting. Choose 3 of the following 4 problems. Remember to work each problem as fully as possible. Partial credit will be given so SHOW ALL OF YOUR WORK!! Constants: c = 3 x 10 8 m/s h = 6.63 x 10 -34 J s = 4.14 x 10 -15 eV s h = h/2 π k = 0 4 1 πε = 8.99 x 10 9 N m 2 /C 2 hc = 1240 eV nm k = Boltzmann’s constant = 1.38 x 10 -23 J/K = 8.61 x 10 -5 eV/K m e = 9.11 x 10 -31 kg λ c = electron Compton wavelength = 2.34 x 10 -15 m a 0 = Bohr radius = 0.0529 nm 1 MeV/c 2 = 1.783 x 10 -30 kg Useful relationships: 2 / 3 2 2 1 2 = a dx e x ax 1. (a) An electron has a de Broglie wavelength of 0.5 nm. Compute its momentum and energy. (10 points) (b) An electron has a de Broglie wavelength of 0.5 fm (1 fm = 10 -15 m). Compute its momentum and energy. (10 points) (c) Prove that the phase velocity of a wave packet is v /2, where v . (13 points)
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exam2_003 - Physics 3101, Introduction to Modern Physics,...

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