Rate constant for a 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 relationship between the rate constant (λ) and the average life (τ) of a reaction, we can break it down into a few clear steps:

### Step-by-Step Solution:

1. **Understanding Rate Constant (λ)**:
- The rate constant (λ) is a proportionality constant that relates the rate of a reaction to the concentration of reactants. It is a key parameter in chemical kinetics.

2. **Understanding Average Life (τ)**:
- The average life (or average lifetime) of a particle or unstable nucleus is the average time it takes for a particle to decay or react. It is a measure of stability.

3. **Relationship Between Average Life and Rate Constant**:
- The average life (τ) is inversely related to the rate constant (λ). This means that as the rate constant increases, the average life decreases, and vice versa.

4. **Formula Derivation**:
- The relationship can be expressed mathematically as:
\[ τ = \frac{1}{λ} \]
- This formula indicates that the average life is equal to the reciprocal of the rate constant.

5. **Conclusion**:
- Therefore, the average life (τ) is represented by the formula \( \frac{1}{λ} \).

### Final Answer:
The average life is represented by \( \frac{1}{λ} \).

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