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) remain after 4 minutes.