How much energy is required to produce the electron-positron pair

  1. 1. The problem statement, all variables and given/known data
    How much energy is required to produce the electron-positron pair in the filed of nucleus (Z=20) if electron is captured to the ground 1s state of the system.

    3. The attempt at a solution

    I can calculate the energy of the captured electron from

    E = - εZ2/(2n2) where ε=me4/hbar2≈27.2eV

    E = - 5442eV

    Now I have to add this energy to the energy of created positron to have total required energy, right ? But I do not know how to find energy of a positron.
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,041
    Science Advisor
    Homework Helper

    hi vst9! :smile:
    won't it be the same as the energy of the electron?
     
  4. hi tiny-tim !

    Yes I think so, then it is the energy and momentum conservation that places a restriction
    on the positron to have the same energy as electron , right ?

    I was a little bit confused by the "... in the filed of nucleus" part of the question, then
    this filed of a nucleus does not change much (except maybe the needed energy).

    So, the needed energy for pair creation is E=2*5442=10.88keV
     
  5. tiny-tim

    tiny-tim 26,041
    Science Advisor
    Homework Helper

    hi vst98! :wink:

    right! :smile:

    i'm not sure why they mentioned the field (not "filed" :wink:) … it doesn't seem to add anything to the rest of the question :confused:
     
  6. Ok, thanks !

    (yes it is "field" and not "filed" in the original question, my flip error :) )
     
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