Question

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).
\(e^++_Z^AX\rightarrow _{Z-1}^AY+v\)
Show that if β⁺ emission is energetically allowed, electron capture is necessarily allowed but not vice-versa.

Answer 1

From equations (1) and (2), it follows that if E₁ > 0, then E₂ > 0
i.e if β⁺emission is energetically allowed, then the electron capture is necessarily allowed. On the other hand, if E₂ > 0, then it does not necessarily mean that E₂ > 0, Thus if the electron capture is allowed, then β⁺emission is not necessarily allowed.