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
Answer & explanation
Correct answer: option 1
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:
$t = \frac{2.303}{k}\log\frac{N_0}{N}$
$t = \frac{2.303}{9.2\times10^{-3}} \log\left(\frac{1}{0.25}\right)$
$\log(4) = 0.602$
$t = \frac{2.303 \times 0.602}{9.2\times10^{-3}}$
$t \approx \frac{1.386}{9.2\times10^{-3}} \approx 150.7\ \text{min}$