Question

The half-life of radon-222 is 3.8 days. How much of a 100 kg sample is left after 15.2 days?

Answer 1

Let t_0 be the half life of a radioactive element. Radioactive decay is modelled as a negative exponential function. Let A_0 be the initial amount of the sample. The amount A of radioactive element in that sample after t days is given by the formula:

$A=A_0e^{-t/t_0}$

Substitute A_0=100kg, t=15.2 d and t_0=3.8d:

$\begin{gathered} A=(100\operatorname{kg})\times e^{-15.2/3.8} \\ =(100\operatorname{kg})\times e^{-4} \\ =(100\operatorname{kg})\times0.0183156\ldots \\ =1.831563\ldots kg \end{gathered}$

Therefore, the amount of radon-222 that is left from a 100kg sample after 15.2 days is, approximately:

$1.83\operatorname{kg}$