For writing expression for energy of photon
For writing expression for kinetic energy of proton
For proving the relationship between the two
Energy of photon, ${\mathit{E}}_{\mathit{p}}=\frac{\mathit{h}\mathit{c}}{\mathit{\lambda }}$
For proton, $\mathit{\lambda }=\frac{\mathit{h}}{\mathit{m}\mathit{v}}$
$\mathit{m}\mathit{v}=\frac{\mathit{h}}{\mathit{\lambda }}$
Kinetic energy of proton,
${\mathit{E}}_{\mathit{k}}=\frac{1}{2}\mathit{m}{\mathit{v}}^2$
${\mathit{E}}_{\mathit{k}}=\frac{1}{2}\frac{{\mathit{h}}^2}{\mathit{m}{\mathit{\lambda }}^2}$
${\mathit{E}}_{\mathit{p}}=\left(\frac{2\mathit{m}\mathit{\lambda }\mathit{c}}{\mathit{h}}\right){\mathit{E}}_{\mathit{k}}$