The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after

Question

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be

Accepted Answer

The activity $A$ is given by $A = A_0 (\frac{1}{2})^{t/T_{1/2}}$. Given $t = 150$ hours and $T_{1/2} = 100$ hours, $\frac{A}{A_0} = (\frac{1}{2})^{150/100} = (\frac{1}{2})^{3/2} = \frac{1}{2\sqrt{2}}$.

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