An x$-$ray photon undergoes Compton scattering from a free electron. The photon has an initial wavelength of $0\mathrm{.}822$ nm$.$ The recoil speed of the electron is $1\mathrm{.}20106$ m$/$s$.$

$($a$)$

What is the Compton shift in the photon's wavelength $($in pm$)?$

pm

$($b$)$

Through what angle is the photon scattered $($in degrees$)$