An X-ray photon with an initial wavelength of is incident on a free electron…
PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
An X-ray photon with an initial wavelength of 0.050nm is incident on a free electron initially at rest in the laboratory frame. After the collision, the photon is detected moving at an angle of 60∘ relative to its original direction.
Useful physical constants are h=6.63×10−34J s, me=9.11×10−31kg, and c=3.00×108m s−1.
(a) Starting from the conditions immediately before and immediately after the collision, set up, but do not solve, a complete system of algebraic equations that determines both the magnitude and direction of the electron's linear momentum after the interaction. Clearly indicate the unknown quantities.
(b) Solve the system from part (a) to obtain the numerical 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 keV of the electron after the collision. Explain briefly why the non-relativistic or relativistic expression for kinetic energy is more appropriate.