An X-ray photon with an initial wavelength of 0.050nm is incident on a free electron that is initially at rest in the lab frame. After the collision the photon is detected moving at an angle of 60∘ relative to its original direction.
Physical constants that may be useful:
• h=6.63×10−34Js
• me=9.11×10−31kg
• c=3.00×108ms−1
(a) Starting from the conditions immediately before and immediately after the collision, set up (but do not yet solve) a complete system of algebraic equations that can be used to determine both the magnitude and direction of the electron’s linear momentum after the interaction. Clearly indicate which physical quantities are unknown in your system.
(b) Solve the system from part (a) to obtain the numerical value of the magnitude of the electron’s linear momentum pe after the collision.
(c) Determine the angle ϕ between the electron’s momentum vector and the original direction of the photon. State whether the electron emerges on the same or the opposite side of the incident photon’s path as the scattered photon.
(d) Calculate the kinetic energy (in \si{keV}) of the electron after the collision. Explain briefly why the non-relativistic expression or the relativistic expression for kinetic energy is more appropriate for this situation.