1. The problem statement, all variables and given/known data Show that, for low energy photons scattered by ultrarelativistic electrons, the cange in frequency of the photon is given by (v'-v) / v = [(Ω'-Ω).β] / [1-Ω'.β] 2. Relevant equations The full/general form of Compton scattering is given by v'/v = (1-Ω.β) / [(1-Ω'β) + hv/(γmc2) (1 - Ω.Ω') ] where v is photon frequency m is electron mass β is electron velocity divided by c c is speed of light γ is Lorentz factor Ω is unit vector of propagation of the photon and primed quantities are those quantities after scattering 3. The attempt at a solution I have attempted the following. For low energy photons, hv << mc2 so that reduces the equation to v'/v = (1-Ω.β) / (1-Ω'β) or (v'-v)/v = [ (1-Ω.β) / [(1-Ω'β) ] - 1 For ultra-relativistic electrons, velocity is almost c, so β = 1 but looking at the target answer it is not helpful to remove β from the equation. I think maybe I am missing something to do with vectors. How do I properly evaluate (Ω'-Ω).β ? Is it just (Ω'-Ω).β = Ω'.β - Ω.β ?