Show that $Delta E / E,$ the fractional loss of energy of a photon during a collision with a particle of mass $m,$ is given by $$ frac{Delta E}{E}=frac{h f^{prime}}{m c^{2}}(1-cos phi) $$ where $E$ is the energy of the incident photon, $f^{prime}$ is the frequency of the scattered photon, and $phi$ is defined as in Fig. $38-5 .$