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, $E_p = \frac{h c}{\lambda}$ For proton, $\lambda = \frac{h}{m v}$ $m v = \frac{h}{\lambda}$ Kinetic energy of proton, $E_k = \frac{1}{2} m v^2$ $E_k = \frac{1}{2} \frac{h^2}{m \lambda^2}$ $E_p = \left(\frac{2 m \lambda c}{h}\right) E_k$