1. The problem statement, all variables and given/known data I need to derive the equation related to the Compton Effect from the equations for momentum and energy conservation. 2. Relevant equations (1) Compton Effect: λ' -λ = h/me(1-cosθ) (2) Conservation of Momentum (x-direction): h/λ= (h/λ')cosθ+γumeucosΦ (3) Conservation of Momentum (y-direction): 0= (h/λ')sinθ+γumeusinΦ (4) Conservation of Energy: h(c/λ)+mec2 = h(c/λ')+γumec2 Where, λ=initial wavelength of a photon λ'= final wavelength of a photon θ= the angle in which an electron scatters Φ= the angle in which the photon scatters u= speed at which electron scatters c= speed of light in a vacuum 3. The attempt at a solution This is a system of equations problem. So I approached the problem by eliminating squaring equations (2) and (3) and eventually eliminating Φ. This gave me [(h/λ-hcosθ/λ')2+ (h2sin2θ)/(λ')2]/γum2u2=1 Things started to get realllly messy from here. I successfully eliminated u, but by that time, the algebra was too far gone to get back to the Compton Effect equation. Any help would be appreciated.