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Deriving the Compton Effect

  1. Sep 28, 2015 #1
    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.
     
  2. jcsd
  3. Sep 30, 2015 #2
    The derivation should not be too messy if you kept track of all the constant factors correctly. you might help yourself by for example combining quantities as h/m0cλ into one symbol say α. Just use care in writing down each expression and persist. Leave the cosines alone and rely on identity relationships to simplify the expressions.
     
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