Chemistry: The Molecular Science (5th Edition)

$t_{1/2}=30\,min$
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=$\frac{2\,h}{4}=30\,min$