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Scattering of Mev particles

  1. Jul 25, 2011 #1
    Hello
    I actually wanted to posted this in the "Homework" section but it is currently working for me..

    The problem is:

    Calculate the cross-section for the scattering of a 10 MeV alpha particle by a gold nucleus [tex]_{79}^{197}Au[/tex] through an angle greater than (a) 10 degrees (b) 20 degrees c 30 degrees.

    My answer:

    I know the relevant equation is:

    [tex]\sigma=\pi(\frac{Zze^{2}}{4\pi\epsilon_{0}mv_{0}^{2}}\cot\frac{\theta}{2})^{2}[/tex]

    so its really just a plug and chug kind of problem... only thing I can't figure out is how to get the value for v_0.... i know that is hidden somewhere in the fact that it is a 10 Mev particle and I assume E=mc^2 plays a roll too.... but trying the following does not provide me with a useful value of v_o:

    [tex]E=mc^{2}+\frac{1}{2}mv_{0}^{2}[/tex]

    neither does:

    [tex]E=\frac{1}{2}mv_{0}^{2}[/tex]

    so my question is, how do I find the value of v_0 given that I know its an alpha particale (so I know its mass) and also that I know its 10Mev particle?

    Many Thanks!
     
  2. jcsd
  3. Jul 25, 2011 #2

    Drakkith

    User Avatar

    Staff: Mentor

    What is "v_0" ?
     
  4. Jul 25, 2011 #3
    v_0 is the initial velocity that the alpha particle has before any interaction with the gold nucleus..
     
  5. Jul 25, 2011 #4
    The correct relativistic relationship between energy and momentum is
    E^2 = p^2 c^2 + m^2 c^4

    Here m is the invariant mass (in the rest frame) and p =mv.
    From this you can find p and then v.
     
  6. Jul 25, 2011 #5
    Thanks! to clarify though, the energy E, that I want to use will be the 10MeV...?
     
  7. Jul 25, 2011 #6
    I think the 10 MeV should be just the kinetic energy. The rest energy of a proton is about 900 MeV so the 10 MeV cannot include the rest mass of the alpha particle.
    The kinetic energy is
    E^2 - m^2 c^4 = p^2 c^2

    Actually at this energy the classic approximation should work quite well as KE<<E.
     
  8. Jul 25, 2011 #7
    thanks, nasu. E=1/2mv^2 was my initial try but I kept making arithmetic mistakes which is why I came on here... took me at least two hours to get the correct answer for the cross-section!
     
  9. Jul 26, 2011 #8

    xts

    User Avatar

    Nope! Rest mass of [itex]\alpha[/itex]-particle is 3.7GeV, so if you are speaking about 10MeV [itex]\alpha[/itex], it is its pure kinetic energy, and you have pretty non-relativistic case.
     
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