Question

Velocity constant for a first order reaction is \( 2 \times 10^{-3} \, \text{s}^{-1} \). The half-life period for this reaction is

Hint:

For a first-order reaction, the half-life is independent of the concentration of the reactant.

Answer 1

Step 1: Formula for half-life period.
For a first-order reaction, the half-life period \( t_{1/2} \) is given by: \[ t_{1/2} = \frac{0.693}{k} \] where \( k \) is the rate constant. Step 2: Calculate half-life.
Given that \( k = 2 \times 10^{-3} \, \text{s}^{-1} \), \[ t_{1/2} = \frac{0.693}{2 \times 10^{-3}} = 3.465 \times 10^3 \, \text{s} \] Step 3: Conclusion.
Hence, the correct answer is (A) \( 3.465 \times 10^3 \, \text{s} \).