For the β + (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 β ⁺ emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.

Question

Philoid · Accepted Answer

The reaction for the electron capture process is given by:

The reaction for the β ⁺ emission is given by:

Considering the atomic mass of the nucleus we get the following Q value equations.

Q_A =

=

And similarly,

Q_B = m

=

Here from these two equations we can see if Q_B > 0, then Q_A > 0 But, If Q_A > 0 that doesn’t imply Q_B > 0

Which means, if β ⁺ emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.