Rate constant for first order reaction is `lambda`. Average life is representative by:

Options

A. `1/lambda`
B. `(In2)/lambda`
C. `lambda/sqrt2`
D. `0.693/lambda`

Answer

To solve the question regarding the average life of a first-order reaction with a rate constant represented as `lambda`, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Average Life**:
- The average life (or average lifetime) of a reactant in a first-order reaction is defined as the average time it takes for half of the reactant to be consumed.

2. **Recall the Formula for Average Life**:
- For a first-order reaction, the average life (τ) is given by the formula:
\[ \tau = \frac{1}{k} \]
where \( k \) is the rate constant.

3. **Substitute the Given Rate Constant**:
- In this problem, the rate constant is given as \( \lambda \). Thus, we can substitute \( k \) with \( \lambda \):
\[ \tau = \frac{1}{\lambda} \]

4. **Identify the Correct Option**:
- Now, we can compare our derived expression \( \tau = \frac{1}{\lambda} \) with the provided options:
- Option 1: \( \frac{1}{\lambda} \)
- Option 2: \( \frac{\ln 2}{\lambda} \)
- Option 3: \( \frac{\lambda}{\sqrt{2}} \)
- Option 4: \( \frac{0.693}{\lambda} \)

- Since \( \ln 2 \) is approximately 0.693, Option 4 can also be rewritten as:
\[ \frac{0.693}{\lambda} = \frac{\ln 2}{\lambda} \]
- However, the exact expression we derived is \( \frac{1}{\lambda} \), which corresponds to Option 1.

5. **Conclusion**:
- Therefore, the average life of the first-order reaction is represented by:
\[ \text{Average Life} = \frac{1}{\lambda} \]
- The correct answer is **Option 1**.