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

Options

A. 693 min
B. 69.3 min
C. 6.93 min
D. 0.693 min

Explanation

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

### Step-by-Step Solution:

1. **Identify the Formula for Half-Life**:
The half-life (\(T_{1/2}\)) of a first-order reaction is given by the formula:
\[ T_{1/2} = \frac{0.693}{k} \]
where \(k\) is the rate constant.

2. **Substitute the Given Rate Constant**:
In this problem, the rate constant \(k\) is given as \(10^{-2} \, \text{min}^{-1}\). We will substitute this value into the half-life formula:
\[ T_{1/2} = \frac{0.693}{10^{-2}} \]

3. **Calculate the Half-Life**:
Now, we perform the calculation:
\[ T_{1/2} = \frac{0.693}{0.01} = 69.3 \, \text{minutes} \]

4. **Conclusion**:
Therefore, the half-life period of the reaction is:
\[ T_{1/2} = 69.3 \, \text{minutes} \]

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

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