Question

The half-life of iodine-131 is 8 days. How much of a one-gram sample will remain after 4 days?

Answer 1

Decay of radioactive materials is exponential in nature. There are three equivalent equations you can use, but perhaps the clearest is \[N(t)=N_{0}\left(\frac{1}{2}\right)^{t/t_{1/2}}\]
where N(t) is the amount of substance remaining after time \(t\), \(N_{0}\) is the original amount, and \(t_{1/2}\) is the half life of the element. So, plug the numbers in and you get

\[N(t)=1\left(\frac{1}{2}\right)^{4/8}=\sqrt{\frac{1}{2}}\]

So the answer is 0.707 grams (to 3 decimal places).