$5.(10$ pts$)$ In $1923,$ Compton demonstrated the particle nature of light through experiments. When Xrays with an energy $0$ are incident on carbon T$,$ electrons are scattered at an angle $$ with the xaxis, and the scattered X$-$rays are measured at an angle $.($a$)(5$pt$)$ Show that the kinetic energy of recoil the electron is $0=02(1$ cos$)1+02(1$ cos$)($b$)(5$ pts$)$ Show that the recoil angle $$ of the electron is cot $=(1+02)$ tan $2$