(a) Derive an expression for the total shift in photon

Chapter 38, Problem 38.40

(choose chapter or problem)

(a) Derive an expression for the total shift in photon wavelength after two successive Compton scatterings from electrons at rest. The photon is scattered by an angle \(\theta_{1}\) in the first scattering and by \(\theta_{2}\) in the second. (b) In general, is the total shift in wavelength produced by two successive scatterings of an angle \(\theta / 2\) the same as by a single scattering of \(\theta\)? If not, are there any specific values of \(\theta\), other than \(\theta=0^{\circ}\), for which the total shifts are the same? (c) Use the result of part (a) to calculate the total wavelength shift produced by two successive Compton scatterings of \(30.0^{\circ}\) each. Express your answer in terms of h/mc. (d) What is the wavelength shift produced by a single Compton scattering of \(60.0^{\circ}\)? Compare to the answer in part (c).