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Rutherford Scattering, relativistic

  1. May 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Asked to calculate the relativistic correction, to the differential scattering cross section which is given by the equation below in terms of E, E0 and θ where E0= .511 MeV.
    with 100MeV electrons from an Au nuclei at certain angles θ.
    2. Relevant equations

    Relativistic correction = [ 1 - (v0)2/c2.sin2(θ/2)]

    3. The attempt at a solution
    I figure the electron energy is kinetic so 100MeV = 1/2 m v2

    and by re-arranging for v i get; v = 200/E0

    then plugging into the formular for v gives, (at 20°=θ)

    [1 - 200/E0c2.0.03 ]

    I'm not sure, first of all if this is correct do far and second of all how to express in terms of E, could it be to use;

    E = √(1-(v/c)2).mc2 and somehow re-arrange?

    Any help would be greatly appreciated.
    Cheers.
     
  2. jcsd
  3. May 15, 2013 #2
    It's not appropriate at all to use the non-relativistic approximation for kinetic energy here.

    I think you should try to solve v/c from
    [tex] E = \frac{E_0}{ \sqrt{1-(v/c)^2}} [/tex]
     
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