$14.$ In a Compton scattering experiment, an x$-$ray photon scatters through an angle of $13\mathrm{.}0$ from a

free electron that is initially at rest. The electron recoils with a speed of $2,280$ km$/$s$.$

a$)$ Calculate the wavelength of the incident photon. $($Ans: $0\mathrm{.}0722$nm$)$

b$)$ Calculate the angle through which the electron scatters. $($Ans: $83\mathrm{.}3)$