A sample of radioactive nuclei has a half life of 5.5 years. The fraction of sample remaining undecayed after 22 years is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6.25%
By the radioactive decay law, the number of undecayed nuclei is halved in every half-life. After \( n \) half-lives the fraction left is
\( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{n} \)
\( \displaystyle n = \frac{t}{T_{1/2}} = \frac{22\,\mathrm{years}}{5.5\,\mathrm{years}} = 4 \)
\( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{4} = \frac{1}{16} = 6.25\% \)