Compton wavelength shift ($\Delta \lambda ={\lambda }_C(1-\cos \theta )$)

For a photon scattered through angle $\theta$ by an initially stationary free electron, exact relativistic conservation of energy and conservation of momentum give $\lambda \prime -\lambda =(h/m_{e}c)(1-\cos \theta )$. Backscatter gives the maximum shift, $2h/(m_{e}c)$, independent of the initial photon wavelength.