The half life of a radioactive substance is 30 s. Calculate the time taken for the sample to decay by \( \frac{3}{4} \)th of its initial value.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 60 s
The decay of a radioactive sample is governed by its half-life: after every half-life the number of undecayed nuclei halves, \( N = N_0\left(\frac{1}{2}\right)^{n} \), where n is the number of half-lives.
Here three-fourths of the sample decays, so one-fourth of the nuclei is left:
\( \displaystyle \frac{N}{N_0} = \frac{1}{4} = \left(\frac{1}{2}\right)^{2} \Rightarrow n = 2 \)
\( t = nT_{1/2} = 2\times30\,\mathrm{s} = 60\,\mathrm{s} \)