A $4\mathrm{.}00$x$10-15$m $($i$.$e$.4\mathrm{.}00$fm$)$ x$-$ray photon is moving East and collides with a stationary proton. After the collision, the x$-$ray photon is travelling due South. Determine:

a$)$ The frequency of the x$-$ray photon after the collision.

b$)$ The kinetic energy of the electron after the collision.

c$)$ The proton's angle of deflection and final momentum.