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Compton Scattering - angle of deflected electron using momentum and energy conservati

  1. Dec 12, 2011 #1
    Incident Photon λ = 0.1050*10^-9
    Angle which photon is scattered (θ) = 60° (relative to intiial direction)

    What angle is the electron scattered relaive to the original direction? (x)


    Okay, so using linear momentum conservation:


    (1) Incident photon momentum (p) = electron momentum (pe) * cos (x) + scattered photon momentum (q) * cos (60)


    And (where λ' is the wavelength after scattering):
    λ-λ' = h/mc (1-cosθ),
    so pe*cos (x) = h/λ - h/λ'*2

    pe*cos(x) = 3.2966*10^-24 (5sf)

    And then usuing the scalar product of : pe = p - q to find pe:
    eq. (2) : pe^2 = p^2+q^2 - 2pqcosθ
    pe = 6.28*10^-24 (3sf)

    Subbing this back into eq (1):
    6.28*10^-24 (cos(x)) = 3.2966*10^-24
    solving, cos (x) = 58.3°

    However,
    When I solve , still using eq (1) , but energy consevation rather than eq. 2 :
    Incident photon energy (E) = Electron KE (A) + Scattered photon energy (B)
    Then E-B= A
    and E-B = hc/Δλ = hc/(2h/mc) = mc^2/2

    Then electron KE = γmc^2 - mc^2 = mc^2/2
    then : γ= 3/2
    and solving γ for v^2, v^2= 5/9(c^2)

    Therefore (pe) =mvλ = 3.056*10^-22 ( 4sf)

    Finally, subbing this back into eq(1) : :confused: :frown:
    pe*cos(x) = 3.2966*10^-24
    3.056*10^-22*cos(x) = 3.2966*10^-24
    and so cos (x) = 0.0107...

    Any help greatly appreciated !Many , many thanks.
     
  2. jcsd
  3. Dec 12, 2011 #2

    Simon Bridge

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    Re: Compton Scattering - angle of deflected electron using momentum and energy conser

    Why not:
    [tex]\frac{hc}{\lambda^\prime}-\frac{hc}{\lambda}[/tex]
     
  4. Dec 12, 2011 #3
    Re: Compton Scattering - angle of deflected electron using momentum and energy conser

    that is genius.
    haha thank you :)
     
  5. Dec 12, 2011 #4

    Simon Bridge

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    Re: Compton Scattering - angle of deflected electron using momentum and energy conser

    No worries - it's easier to spot these things in someone elses work than in your own.
     
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