Question

A sample of Bismuth-212 has a mass of 2.64 grams (g) after 121 seconds (s). What was the initial mass of the sample if Bismuth-212 has a half-life of 60.5 s?

Answer 1

The mass of a radioactive element at time t is given by
$m(t) = m_0 ( \frac{1}{2} )^{ \frac{t}{t_{1/2}} }$
where $m_0$ is the mass at time zero, while $t_{1/2}$ is the half-life of the element.

In our problem, $m(t)=2.64 g$, t=121.0 s and $t_{1/2}=60.5 s$, so we can find the initial mass $m_0$:
$m_0= \frac{m(t)}{ (\frac{1}{2})^{t/t_{1/2}} } = \frac{2.64 g}{( \frac{1}{2} )^{121/60.5}} =4 \cdot 2.64 g=10.56 g$