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How much energy a photon has to have the momentum of a 10MeV proton

  1. Sep 8, 2009 #1

    ckp

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    How much energy must a photon have if it is to have the same momentum of a 10-MeV proton?

    I am not sure how to go about starting this one. Can someone help me out?
     
  2. jcsd
  3. Sep 8, 2009 #2

    JesseM

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    Good general formula to know in SR:

    [tex]E^2 = m^2 c^4 + p^2 c^2[/tex]

    Where E is the energy, m is the rest mass, and p is the relativistic momentum. You can see that for p=0 this reduces to E=mc^2. And for a photon, the rest mass m is zero, so this reduces to E=pc.

    Meanwhile, for a particle with nonzero rest mass, the relativistic momentum is given by [tex]p = \gamma mv[/tex], where v is the velocity and [tex]\gamma = 1/\sqrt{1 - v^2/c^2}[/tex]

    If you know a proton's rest mass m and energy E, you should be able to use these formulas to find its momentum...
     
  4. Sep 8, 2009 #3

    ckp

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    so E^2 = m^2c^4+p^2c^2

    my E^2 is less than my m^2c^4(the 10MeV is less than the mc^2 for a proton) so my p^2c^2 turns out negative. What am I doing wrong?
     
  5. Sep 8, 2009 #4

    ckp

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    anyone?
     
  6. Sep 8, 2009 #5

    rl.bhat

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    First of all find the momentum of proton having energy 10-MeV, using the formula
    p = sqrt(2mE) where m is the mass of the proton. Then using E = pc find the energy of the photon.
     
  7. Sep 8, 2009 #6

    ckp

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    Where did you get p = sqrt(2mE)?
     
  8. Sep 8, 2009 #7

    rl.bhat

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    p = mv
    p^2 = m^2v^2
    = 2*m*1/2*m*v^2
    = 2*m*E
    So p = sqrt(2mE)
     
  9. Sep 9, 2009 #8

    JesseM

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    Maybe 10 MeV refers to the kinetic energy, which is just the total energy minus the rest mass energy? I'm not sure what the convention when talking about high-energy particles. But it works out that [tex]E^2 = m^2 c^4 + p^2 c^2[/tex] is equivalent to [tex]E = \gamma mc^2[/tex], so the kinetic energy is [tex]KE = (\gamma - 1) mc^2[/tex].
     
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