An X-ray scattering from an electron with negligible initial kinetic energy is observed to undergo a change in wavelength by 2.561 pm. i.e. The scattered X-ray photon has a wavelength 2.561 pm larger than the incident X-ray photon.

Question

 
Find the direction of propagation of the scattered electron relative to the direction of the incident X-ray, given that the incident X-ray has a wavelength of 0.3276 nm.  (i.e. Find the electron scattering angle in degrees.)
 
(Take the Compton wavelength of the electron to be 2.424 pm.  Use the Compton formula, and both components of momentum conservation.  You should work algebraically as far as possible, and hence should only need the Compton wavelength of the electron in terms of physical constants.  In order: find the final photon wavelength and the photon scattering angle.  Store those two values to high precision.  I then suggest algebraically eliminating the unknown electron momentum magnitude from the two momentum conservation equations in favor of the electron scattering angle.  Solve for the electron scattering angle in terms of the photon scattering angle and the initial and final photon wavelengths. The final algebraic equation is not very difficult.)