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Momentum - Energy Question

  1. Dec 15, 2007 #1
    So, I am reading about a compton scattering problem, and I don't understand part of the derivation of a formula. I will explain my confusion.

    If a gamma photon with energy [tex]E_{\gamma}[/tex], undergoes compton scattering with an electron which is at rest, how does one arrive at the following expression?


    So far it says we start with the conservation of energy and momentum:
    [tex]E_{\gamma}=E^{'}_{\gamma}+E_{e} \ \ (eqn 1)[/tex]
    [tex]\frac{E_{\gamma}}c=P_{e}-\frac{E^{'}_{\gamma}}{c}\ \ (eqn 2)[/tex]

    From eqn 2 we get:

    This is where I am confused. I don't understand where the term inside of the radical comes from. Any ideas?
  2. jcsd
  3. Dec 15, 2007 #2


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    Staff: Mentor

    The [itex]E_e[/itex] in the square root on the right is the electron's kinetic energy, which most books call [itex]K_e[/itex]. [itex]E_e[/itex] usually means the total energy:

    [tex]E_e = K_e + m_0 c^2[/tex]

    Using this notation, the relationship between energy, momentum and mass is

    [tex]E^2 = (pc)^2 + (m_0 c^2)^2[/tex]


    [tex]p_e c = \sqrt {E_e^2 - (m_0 c^2)^2} = \sqrt {(K_e + m_0 c^2)^2 - (m_0 c^2)^2}[/tex]
    Last edited: Dec 15, 2007
  4. Dec 17, 2007 #3
    hi all,

    a similar post for me. pls help me.
    i need to calculate the energy lost by a solid sphere (~ 0.5 mm dia) on hitting the solid wall obliquely.
    i know the tangetial and normal velocities and the restitution coefficients. what other parameters do i need to know ??

    help with the expression or a reference to articles in the web would be of great help.

    thanks you.
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