where we note that φ= π(since the photon is scattered back in the direction of incidence). Now, from the Doppler shift formula (Eq. 38-25) the frequency f'0of the photon prior to the scattering in the new reference frame satisfies fcf'',00011==+−λβwhere = v/c. Also, as we switch back from the new reference frame to the original one after the scattering 11.cff−−′′+λ+We solve the two Doppler-shift equations above for λ'and λ'0and substitute the results into the Compton shift formula for ∆λ': ∆λ'.=−+−−+=11202hmceSome simple algebra then leads to Ehf hfhe++−FHGIKJ−0211211.84. The difference between the electron-photon scattering process in this problem and the
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