For 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.

Let the amount of energy released during the electron capture process beQ1. The nuclear reaction can be written as: Let the amount of energy released during the positron capture process beQ2. 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 ifQ2> 0, thenQ1> 0; Also, ifQ1> 0, it does not necessarily mean thatQ2> 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 theQ-value must be positive for an energetically-allowed nuclear reaction. read less