HW-1 - of u ( , T ) as a function of . (cp. SSM, problem...

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Physics 17 Due 10-05-09 Fall 2009 T. Tomboulis HOMEWORK # 1 Reading Assignment: Review Special Relativity energy-momentum relations: SMM, Ch. 2, Summary p. 59. SMM: Ch. 3: Sections 3.1 - 3.6. Problems: 1. Consider the black body radiation curves (Figure 3.3 in SMM). One notes that as T increases, the wavelength λ max at which u ( λ, T ) reaches its maximum shifts towards shorter wavelengths (body shifts from glowing red towards blue). (a) Show that indeed the following relation ( Wien’s displacement law ) holds: λ max T = constant = hc k C , where C is a numerical constant. (b) Give a numerical value for C . Hint: Start with Planck’s law (equation (3.9) in SMM), and rewrite it in terms of λ (equation (3.20)) - show how this is done. Then apply the condition for a maximum
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Unformatted text preview: of u ( , T ) as a function of . (cp. SSM, problem 5). 2. SMM Ch. 3: Problem #14 3. SMM Ch. 3: problem #20 4. SMM Ch. 3: Problem #24 5. SMM Ch. 3: Problem #47 (Head-on collision means the photon backscatters, i.e. = 180 in the Compton scattering formula.) 6. Carry out the sums involved in obtaining the average energy of a Planck oscillator in the derivation of Plancks law, i.e. show that E = X n =0 E n e-E n /kT X n =0 e-E n /kT 1 = X n =0 nhf e-nhf/kT X n =0 e-nhf/kT = hf e hf/kT-1 . Hint: Recall the geometrical series result X n =0 r n = 1 1-r , r < 1 . 2...
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This note was uploaded on 01/21/2010 for the course PHYS 17 taught by Professor Staff during the Fall '08 term at UCLA.

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HW-1 - of u ( , T ) as a function of . (cp. SSM, problem...

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