The ratio of parent to daughter isotopes in a radioactive decay process is 0.40.How many half-lives have elapsed since the material was 100% parent atoms?
A)less than l
B)more than 3
C)between l and 2
D)between 2 and 3

Question

Quizplus · Accepted Answer

The ratio of parent to daughter isotopes in a radioactive decay process is given by $R=\frac{N_p}{N_d}$, where $N_p$ is the number of parent atoms and $N_d$ is the number of daughter atoms. The ratio $R$ is related to the number of half-lives $t$ that have elapsed since the material was 100% parent atoms by the equation $R=(\frac{1}{2})^t$.

In this problem, $R=0.40$, so $(\frac{1}{2})^t=0.40$. Taking the logarithm of both sides with base $\frac{1}{2}$, we get $t=\frac{\log 0.40}{\log 0.5} \approx 1.32$. Therefore, the number of half-lives elapsed is between 1 and 2, i.e. the best choice is C.

The Ratio of Parent to Daughter Isotopes in a Radioactive