Consider the Compton effect. We direct a beam of $2\mathrm{.}01$MeV photons toward some material. Many of the photons collide with electrons in the material, ejecting the electrons from the material. The collisions also cause the photons to be scattered in a variety of directions, each scattered photon having less energy than it had initially.

$($a$)$

Find the wavelength of the photons in the initial beam.

pm $(0\mathrm{.}004$ pm$)$

$($b$)$

Consider a particular collision where the scattered photon comes out at an angle of $135\mathrm{.}5$ with respect to its initial direction. Find the wavelength of this scattered photon.

pm $(0\mathrm{.}03$ pm$)$

$($c$)$

Find its energy.

MeV $(0\mathrm{.}02$ MeV$)$

$($d$)$

Find the kinetic energy of the electron this photon collided with.

MeV $(0\mathrm{.}03$ MeV$)$