A first order reaction has a half-life of 693 sec. What will be its rate constant?

0.001 $sec^{-1}$

The correct answer is Option (3) → 0.001 $sec^{-1}$.

For a first-order reaction, the relationship between the half-life (\(t_{1/2}\)) and the rate constant (\(k\)) is given by the formula:

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

Where:

\(t_{1/2}\) is the half-life of the reaction,

\(k\) is the rate constant.

Given:

Half-life (\(t_{1/2}\)) = 693 seconds

Rearranging the formula to find the rate constant \(k\):

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

Substituting the given half-life into the equation:

\(k = \frac{0.693}{693 \, \text{sec}} = 0.001 \, \text{sec}^{-1}\)

Conclusion:

The rate constant \(k\) for the reaction is 0.001 sec⁻¹.

Thus, the correct answer is 0.001 sec⁻¹.