p41_040 - 40. (a) and (b) Let the wavelength of the two...

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40. (a) and (b) Let the wavelength of the two photons be λ 1 and λ 2 = λ 1 +∆ λ . Then, eV = hc λ 1 + hc λ 1 +∆ λ , or λ 1 = (∆ λ/λ 0 2) ± p (∆ λ/λ 0 ) 2 +4 2 / λ . Here, ∆ λ = 130 pm and λ 0 = hc/eV = 1240 keV · pm / 20 keV = 62 pm . The result of problem 3 in Chapter 39 is adapted to these units ( hc = 1240 eV · nm = 1240 keV · pm). We choose the plus sign in the expression for λ 1 (since λ 1 > 0) and obtain λ 1 = (130 pm / 62 pm 2) + p (130 pm / 62 pm) 2 +4 2 / 62 pm
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