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

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vst98
#1
Feb25-12, 04:09 PM
P: 32
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.
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tiny-tim
#2
Feb25-12, 04:44 PM
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hi vst9!
Quote Quote by vst98 View Post
But I do not know how to find energy of a positron.
won't it be the same as the energy of the electron?
vst98
#3
Feb26-12, 03:03 PM
P: 32
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

tiny-tim
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Feb26-12, 04:41 PM
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How much energy is required to produce the electron-positron pair ...

hi vst98!

right!

i'm not sure why they mentioned the field (not "filed" ) it doesn't seem to add anything to the rest of the question
vst98
#5
Feb27-12, 05:18 PM
P: 32
Ok, thanks !

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


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