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Pair production problem

  1. May 18, 2017 #1
    1. The problem statement, all variables and given/known data

    A proton and anti-proton are created by a photon with wavelength λ= 6.607×10−7 nm. What is the magnitude of the velocity of the newly created proton and anti-proton pair? Note, the mass of a proton/anti-proton is mp= 1.673×10-27 kg = 938.3M MeV/c2.

    2. Relevant equations

    Ephoton = h ⋅ c / λ
    E0 = m0 ⋅ c2
    KE = 0.5 ⋅ m ⋅ v2

    3. The attempt at a solution

    Ephoton= 3.009 x 10-10 J
    E0 = 1.506 x 10-10 J

    KE=Ephoton - 2 ⋅ E0 / (2)
    KE= 3.009 x 10-10 - 2 ⋅ 1.506 x 10-10 J / (2)
    KEof either particle= -1.5 x 10-13 J
     
    Last edited: May 18, 2017
  2. jcsd
  3. May 18, 2017 #2

    Bandersnatch

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    Google calculator shows 938.3 MeV=1.503E-10 Joules.
     
  4. May 18, 2017 #3
    if you convert the energy of the photon to Mev and subtract from it (2*938.3 Mev) it will give a positive number
    i guss the problem is the mass of the proton missing a lot of digits and the speed of light as well.
    like Bandersnatch said if you use the full digits of the mass and speed of light it will give 1.503*10^-10
     
  5. May 18, 2017 #4
    I calculated E0 using E0 = m0 ⋅ c2. So is that the same as the given value?
     
  6. May 18, 2017 #5
    You are right. I converted both to MeV and it came out to KE = 0.029!

    0.029 MeV ---> 4.646 x10-15 J

    I calculate that the speed is 2.36 x 106 m/s.

    However after using more sig fig digits the answer goes to 0 m/s. Maybe this is a relativistic problem that needs a different equation?
     
    Last edited: May 18, 2017
  7. May 18, 2017 #6

    haruspex

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    That seems rather unlikely. If you cannot find a mistake please post all your working.
     
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