What will be the half life of a radioactive isotope whose \( \displaystyle\frac{1}{16} \)th of initial amount remains undecayed after 2 hours?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30 min
The amount of a radioactive isotope left after n half-lives is \( N = N_0\left(\frac{1}{2}\right)^{n} \).
\( \displaystyle \frac{N}{N_0} = \frac{1}{16} = \left(\frac{1}{2}\right)^{4} \Rightarrow n = 4 \)
Four half-lives take 2 hours = 120 min.
\( \displaystyle T_{1/2} = \frac{120\,\mathrm{min}}{4} = 30\,\mathrm{min} \)