$37$ Rutherford equals

$\beta$-decay means emission of electron from

Actinium $231$,${}^{231}Ac_{89}$,emits in succession two $\beta^-$ particles,four $\alpha$ particles,one $\beta^-$ particle,and one $\alpha$ particle,plus several $\gamma$ rays. What is the resultant isotope?

Which of the following is a correct statement?

Beta rays emitted by a radioactive material are

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.