Consider a monochromatic beam of photons with initial energy that scatter from free
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics
Problem
Consider a monochromatic beam of photons with initial energy E0 that scatter from free, stationary electrons at an angle θ. Assume relativistic effects for the electrons can be neglected except as required by conservation laws.
(a) Show algebraically that the scattered photon’s wavelength can be written in the form λ′=λ0+A(1−cosθ), where A is a constant to be identified.
(b) Using the result from part (a), derive an explicit expression for the scattered photon’s energy E′ in terms of E0, θ, and known physical constants.
(c) Obtain an approximate expression for E′ that is valid for small scattering angles (θ ≪ 1 rad) and discuss the physical significance of the limiting form.