1. The problem statement, all variables and given/known data Compton scattering can be used both to measure the direction and energy of photons in nuclear physics experiments. For a particular preparation a spectrum of Compton scattered electrons was measured which clearly corresponded to a generally monochromatic gamma radiation. The maximum electron energy was measured to 150 keV. Calculate the wavelength of the incoming monochromatic radiation. 2. Relevant equations What do I know : Compton formula : λ'-λ = (h/mc) * (1-cos(θ)) Energy conservation: hc/λ + m * c^2 = hc/λ' +γ*m *c^2 E_befor = hc/λ , E_after = hc/λ' 3. The attempt at a solution The correct solution is : E_max = 150 keV = 2.4 * 10-14 λ'-λ = (h/mc) * (1-cos(θ)) and maximum occurs when cosθ = -1 then : λ'-λ = 2*(h/mc) Further we have : E_befor + m * c2 = E_after + γ*m *c2 E_befor - E_after = (γ-1)mc2 = E_kinetic E_kinetic = hc((1/λ)-(1/λ')) † We take E_kinetic = 150 keV = 2.4 * 10-14 and solve λ'= 2*(h/mc) + λ and just put everthing in † and solve λ which is = 0.044nm My question is why can't we solve this by thinking : hc/λ + m * c^2 = hc/λ' +γ*m *c^2 = Constant = 2.4 * 10-14 J and just take hc/λ + m * c^2 = 2.4 * 10-14 J ? I dont get the same λ as the solution and I know it's wrong but why is this wrong?!