NEET-XII-Physics
13: Nuclei
- #22For the
(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.
Ans : 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.