If the rate constant for the first order reaction is $2 ×10^{-5}\, s^{-1}$, then the half-life will be

577.5 min

The correct answer is Option (1) → 577.5 min

For a first-order reaction, the half-life is given by:

$t_{1/2} = \frac{0.693}{k}$

Given:

$k = 2 \times 10^{-5}\ \text{s}^{-1}$

$t_{1/2} = \frac{0.693}{2 \times 10^{-5}} = 34650\ \text{s}$

Convert seconds to minutes:

$\frac{34650}{60} = 577.5\ \text{min}$