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Homework Help: Energy and Compton scattering

  1. May 19, 2017 #1
    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?!
  2. jcsd
  3. May 19, 2017 #2


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    Staff Emeritus
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    Why would the maximum electron energy be equal to the total energy of the photon-electron system? That's what you're claiming in your method.
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