1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...