Some radioactive nucleus may emit

For the $\beta^{+}$ (positron) emission from a nucleus,there is another competing process known as electron capture (an electron from an inner orbit,say,the $K$-shell,is captured by the nucleus and a neutrino is emitted).
$_{z}^{A} X + e^{-} \rightarrow _{z-1}^{A} Y + \nu$
Show that if $\beta^{+}$ emission is energetically allowed,electron capture is necessarily allowed,but not vice-versa.

During a $\beta^{-}$-decay,

The modern treatment method $P.E.T.$ is based on:

In the nuclear reaction $_{85}X^{297} \to Y + 4\alpha$,$Y$ is:

Curie is a unit of