# Question #67ffa

Dec 15, 2017

$139.32$ seconds

#### Explanation:

If only 4% of the original sample remains, we know that:

$\frac{100}{2} ^ n = 4$, where $n$ is the number of half-lives elapsed.

Rearranging this gives

${2}^{n} = 25$
$n = {\log}_{2} \left(25\right)$
$n = 4.64386$ half lives

Since a half-life of Radium-221 is 30 seconds, we know it must have taken 4.6439*30 seconds for 96% to decay, which is $139.32$ seconds.