The half life of a radioactive nuclide is 20 hours. What fraction of original activity will remain after 80 hours?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{1}{16} \)
The activity of a sample is proportional to the number of undecayed nuclei, \( R = \lambda N \), so it falls by the same factor as \( N \). In each half-life it is halved, so after \( n \) half-lives
\( \displaystyle \frac{R}{R_0} = \left(\frac{1}{2}\right)^{n} \)
\( \displaystyle n = \frac{t}{T_{1/2}} = \frac{80\,\mathrm{h}}{20\,\mathrm{h}} = 4 \)
\( \displaystyle \frac{R}{R_0} = \left(\frac{1}{2}\right)^{4} = \frac{1}{16} \)