A radioactive substance decays to \( \frac{1}{8} \)th of its initial activity in 30 days. The half life of the radioactive substance expressed in days is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10
The activity of a radioactive substance halves in every half-life, so after n half-lives it is \( A = A_0\left(\frac{1}{2}\right)^{n} \).
\( \displaystyle \frac{A}{A_0} = \frac{1}{8} = \left(\frac{1}{2}\right)^{3} \Rightarrow n = 3 \)
Three half-lives take 30 days.
\( \displaystyle T_{1/2} = \frac{30\,\mathrm{days}}{3} = 10\,\mathrm{days} \)