Consider an elastic collision between a photon with initial wavelength 0 moving in the x-direction and a stationary electron, as depicted in Fig. 34.9b.

Consider an elastic collision between a photon with initial wavelength λ₀ moving in the x-direction and a stationary electron, as depicted in Fig. 34.9b. Use relativistic expressions for energy and momentum from Chapter 33 to show that conservation of energy and momentum yield the equations hc/λ₀ + mc² = hc/λ + γmc² , h/ λ₀ = (h/ λ) cosθ + γmu cosϕ, and 0 = (h/ λ) sinθ - γmu sinϕ, where λ is the post-collision photon wavelength and the angles θ and ϕ are as shown in Fig. 34.9b. Solve these equations to find the Compton shift (Equation 34.8).

1 - cose) (Compton shift) (34.8) mc