A radioactive element decays to 1/64th of its initial activity in 30 days. Its half life is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5 days
The activity of a radioactive sample halves in every half-life, so after n half-lives it is \( R = R_0\left(\frac{1}{2}\right)^{n} \).
\( \displaystyle \frac{R}{R_0} = \frac{1}{64} = \left(\frac{1}{2}\right)^{6} \Rightarrow n = 6 \)
Six half-lives take 30 days.
\( \displaystyle T_{1/2} = \frac{30\,\mathrm{days}}{6} = 5\,\mathrm{days} \)