A first order reaction has a half-life period of `34.65` seconds. Its rate constant is

Options

A. `2xx10^(-2)sec^(-1)`
B. `4xx10^(-4)sec^(-1)`
C. `20sec^(-1)`
D. `2xx10^(-4)sec^(-1)`

Explanation

To find the rate constant (k) for a first-order reaction given its half-life (T_half), we can use the formula:

\[ T_{1/2} = \frac{0.693}{k} \]

### Step-by-Step Solution:

1. **Identify the given data**:
- The half-life (T_half) of the reaction is given as 34.65 seconds.

2. **Use the half-life formula for first-order reactions**:
- The formula relating half-life to the rate constant for a first-order reaction is:
\[ T_{1/2} = \frac{0.693}{k} \]

3. **Rearrange the formula to solve for k**:
- To find the rate constant (k), we can rearrange the formula:
\[ k = \frac{0.693}{T_{1/2}} \]

4. **Substitute the value of T_half into the equation**:
- Substitute T_half = 34.65 seconds into the equation:
\[ k = \frac{0.693}{34.65} \]

5. **Calculate the value of k**:
- Performing the calculation:
\[ k = \frac{0.693}{34.65} \approx 0.0200 \, \text{s}^{-1} \]

### Final Answer:
The rate constant (k) for the reaction is approximately \( 0.0200 \, \text{s}^{-1} \).