For the $\beta^{+}$ (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). $e^{+} + \,{}^{A}_{Z}X$ → $\,{}^{A}_{Z-1}Y + v$ Show that if $\beta^{+}$ emission is energetically allowed, electron capture is necessarily allowed but not vice-versa.