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Relativistic Mechanics (momentum)

  1. Sep 20, 2009 #1
    I did the problem, though I don't think that it is right. I think that the number is to big so I think I might have screwed up somewhere though I don't know where.

    1. The problem statement, all variables and given/known data
    What is the momentum (in units of MeV/c) of an electron with a kinetic energy of 1.00 MeV?

    2. Relevant equations
    Energy[tex]_{kinetic}[/tex] = Energy
    E[tex]^{2}[/tex] = m[tex]^{2}_{0}[/tex]c[tex]^{4}[/tex] + p[tex]^{2}[/tex]c[tex]^{2}[/tex]
    c = 3E8 m/s
    m0 = rest mass = .511 MeV c[tex]^{-2}[/tex]

    3. The attempt at a solution
    E[tex]^{2}[/tex] = m[tex]^{2}_{0}[/tex]c[tex]^{4}[/tex] + p[tex]^{2}[/tex]c[tex]^{2}[/tex]
    p[tex]^{2}[/tex]c[tex]^{2}[/tex] = m[tex]^{2}_{0}[/tex]c[tex]^{4}[/tex] - E[tex]^{2}[/tex]
    p[tex]^{2}[/tex]c[tex]^{2}[/tex] = (.511 MeV c[tex]^{-2}[/tex])[tex]^{2}[/tex](3x10[tex]^{8}[/tex]m/s)[tex]^{4}[/tex] - (1.00 MeV)[tex]^{2}[/tex]
    p[tex]^{2}[/tex]c[tex]^{2}[/tex] = 2.35E16 MeV[tex]^{2}[/tex]
    pc = 1.53E8 MeV
    p = 1.53E8 MeV c[tex]^{-1}[/tex]
     
    Last edited: Sep 20, 2009
  2. jcsd
  3. Sep 20, 2009 #2
    Firstly, [tex]p^{2} c^{2} = E^{2} - m_{0}^{2} c^{4}[/tex] - rearrange your terms carefully.

    Next, [tex]( 0.511 MeV c^{-2} )^{2} ( c^{4} ) = 0.511 MeV^{2}[/tex]
    Note that the [tex]c^{-2}[/tex] is also squared!
     
  4. Sep 20, 2009 #3
    OK, thanks for your help, though the left and the right side of the equations are not matching up when I go to plug the answers back in.

    I got that p = .8596 MeV c-1

    Plugging it back in, I get
    p2c2 = E - m02c4
    (.8596 [STRIKE]c-1[/STRIKE])2[STRIKE]c2[/STRIKE] = 1 - (.26112 MeV2 [STRIKE]c-4[/STRIKE])[STRIKE]c4[/STRIKE]
    .7389 = .2611
     
  5. Sep 20, 2009 #4
    Err..it should be 0.7389 = 1 - 0.2611 *points to your 2nd last equation* which is coherent.
     
  6. Sep 20, 2009 #5
    My bad, I'm a retard today... Thanks for your help (I forgot that the 1 was there...)
     
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