(a) The number of nuclei of a given radioactive sample at time $\mathit{t}=0$ and $\mathit{t}=\mathit{T}$ are ${\mathrm{N}}_0$ and $\frac{{\mathrm{N}}_0}{\mathit{n}}$ respectively. Obtain an expression for the half-life $\left({\mathit{T}}_{1∕2}\right)$ of the nucleus in terms of $\mathit{n}$ and T.
(b) Write the basic nuclear process underlying ${\mathit{\beta }}^{-}$ decay of a given radioactive nucleus.