A first order reaction is found to have rate constant, k = 3.0 × 10^-…

The correct answer is Option (3) → 2.31 s

For a first order reaction the integrated rate law gives the half-life directly. At \( t_{1/2} \) the concentration has dropped to half, so:

    \( \displaystyle k = \frac{2.303}{t_{1/2}}\log\frac{[\mathrm{R}]_0}{[\mathrm{R}]_0/2} = \frac{2.303 \log 2}{t_{1/2}} \)

    \( \displaystyle t_{1/2} = \frac{0.693}{k} \)

The half-life of a first order reaction is independent of the initial concentration. With \( k = 3.0 \times 10^{-1}\ \mathrm{s^{-1}} \):

    \( \displaystyle t_{1/2} = \frac{0.693}{0.30\ \mathrm{s^{-1}}} = 2.31\ \mathrm{s} \)

So the half-life is 2.31 s.

Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.

NCERT (2026-27 edition):
Half-Life of a Reaction – “A first order reaction is found to have a rate constant, k = 5.5 × 10^-14 s^-1. Find the half-life of the reaction.”