The half life of a radioactive substance is 20 s. The time taken for its sample to decay \( 7/8^{\mathrm{th}} \) of the initial value
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 60 s
After each half-life the number of undecayed nuclei is halved, so after \( n \) half-lives \( N = N_0/2^{n} \).
If \( 7/8 \) of the sample has decayed, \( 1/8 \) is left.
\( \displaystyle \frac{N}{N_0} = \frac{1}{8} = \left(\frac{1}{2}\right)^{n} \;\Rightarrow\; n = 3 \)
\( \displaystyle t = n\,T_{1/2} = 3\times20 = 60\,\mathrm{s} \)