E_{e} = E_{γ} − E_{ionization}

(γ − 1)m_{e}c^{2} = 662 keV
(γ − 1)(511 keV) = 662 keV

E′_{γ} = E_{γ}(\frac{m_{e}c^{2}}{m_{e}c^{2} + E_{γ}(1 − cos θ)})

\begin{aligned}E′_{e} & = E_{γ} − E′_{γ} \\ & = E_{γ} [1 − (\frac{m_{e}c^{2}}{m_{e}c^{2} + E_{γ}(1 − cos θ)})] \end{aligned}