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 $1,960$ km$/$s$.$

$($a$)$ Calculate the wavelength of the incident photon.

Your response differs from the correct answer by more than $10\%.$ Double check your calculations. nm

$($b$)$ Calculate the angle through which the electron scatters.