A radioactive substance decays with a rate constant of $9.2 × 10^{-3} min^{-1}$. Time taken for 75% of the sample to decompose is

150.7 min

The correct answer is Option (1) → 150.7 min

Radioactive decay follows first-order kinetics.

Given:

Rate constant

$k = 9.2 \times 10^{-3}\ \text{min}^{-1}$

For 75% decomposition, only 25% remains:

$\frac{N}{N_0} = 0.25$

First-order equation:

$t = \frac{2.303}{k}\log\frac{N_0}{N}$

$t = \frac{2.303}{9.2\times10^{-3}} \log\left(\frac{1}{0.25}\right)$

$\log(4) = 0.602$

$t = \frac{2.303 \times 0.602}{9.2\times10^{-3}}$

$t \approx \frac{1.386}{9.2\times10^{-3}} \approx 150.7\ \text{min}$