The rate constant of first order reaction is `10^(-2)"min"^(-1)`. The half-life period of reaction is

Options

A. 69.3 min
B. 34.65 min
C. 17.37 min
D. 3.46 min

Explanation

To find the half-life period of a first-order reaction with a given rate constant, we can use the formula for the half-life of a first-order reaction:

### Step-by-Step Solution:

1. **Identify the given data:**
- The rate constant (k) for the first-order reaction is given as \( k = 10^{-2} \, \text{min}^{-1} \).

2. **Use the formula for half-life of a first-order reaction:**
- The formula for the half-life (\( T_{1/2} \)) of a first-order reaction is:
\[ T_{1/2} = \frac{0.693}{k} \]

3. **Substitute the value of k into the formula:**
- Plugging in the value of \( k \):
\[ T_{1/2} = \frac{0.693}{10^{-2}} \, \text{min} \]

4. **Calculate the half-life:**
- Simplifying the expression:
\[ T_{1/2} = 0.693 \times 10^{2} \, \text{min} = 69.3 \, \text{min} \]

5. **Conclusion:**
- The half-life period of the reaction is \( 69.3 \, \text{min} \).

### Final Answer:
The half-life period of the reaction is **69.3 minutes**.

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