Answer
$t_{1/2}=30\,min$
Work Step by Step
Let $R$ be the final activity and $R_{0}$ be the initial activity.
Given: $R=\frac{1}{16}R_{0}$
We know that after one half-life, $R=\frac{1}{2}R_{0}$,
after two half-lives, $R=(\frac{1}{2})^{2}\times R_{0}$ and
after 4 half-lives, $R=(\frac{1}{2})^{4}\times R_{0}=\frac{1}{16}R_{0}$.
$\implies$ 4 half-lives=2 hours
Or 1 half-life=$\frac{2\,h}{4}=30\,min$
