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(positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K−shell, is captured by the nucleus and a neutrino is emitted). 
Show that if emission is energetically allowed, electron capture is necessarily allowed but not vice−versa.
Asked by Divya Last Modified
Answer 
Shivam Sharma
Let the amount of energy released during the electron capture process be Q1. The nuclear reaction can be written as:
Let the amount of energy released during the positron capture process be Q2. The nuclear reaction can be written as:
= Nuclear mass of 
= Nuclear mass of 
= Atomic mass of
= Atomic mass of
me = Mass of an electron
c = Speed of light
Q-value of the electron capture reaction is given as:
Q-value of the positron capture reaction is given as:
It can be inferred that if Q2 > 0, then Q1 > 0; Also, if Q1> 0, it does not necessarily mean that Q2 > 0.
In other words, this means that ifemission is energetically allowed, then the electron capture process is necessarily allowed, but not vice-versa. This is because the Q-value must be positive for an energetically-allowed nuclear reaction.
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