Assertion In one half-life of a radioactive substance more number of nuclei are decayed than in one average life.
Reason Average life = Half -life/in (2)

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the question, we need to analyze the assertion and the reason provided:

### Step 1: Understanding the Assertion
The assertion states that "In one half-life of a radioactive substance, more number of nuclei are decayed than in one average life."

### Step 2: Understanding the Reason
The reason states that "Average life = Half-life / ln(2)." This relationship is a known fact in nuclear physics.

### Step 3: Definitions
1. **Half-life (T₁/₂)**: The time required for half of the radioactive nuclei in a sample to decay.
2. **Average life (τ)**: The average time a nucleus exists before decaying, which is mathematically defined as τ = 1/λ, where λ is the decay constant.

### Step 4: Mathematical Relationships
From the reason, we know:
\[ \text{Average life} (τ) = \frac{\text{Half-life} (T_{1/2})}{\ln(2)} \]

This implies that:
\[ τ > T_{1/2} \]
because ln(2) is approximately 0.693, which is less than 1.

### Step 5: Decay Calculation
1. **Number of Nuclei Decayed in Half-life**:
- If we start with \( N_0 \) nuclei, after one half-life, the number of remaining nuclei is:
\[ N_{t} = N_0 e^{-\lambda T_{1/2}} = N_0 \cdot \frac{1}{2} \]
- Thus, the number of decayed nuclei in one half-life is:
\[ N_0 - N_{t} = N_0 - \frac{N_0}{2} = \frac{N_0}{2} \]

2. **Number of Nuclei Decayed in Average Life**:
- The average life is longer than the half-life, and over this time, more nuclei will have decayed.
- The number of nuclei remaining after one average life is:
\[ N_{t} = N_0 e^{-\lambda τ} \]
- Since τ > T₁/₂, more than half of the original nuclei will have decayed during the average life.

### Step 6: Conclusion
From the calculations, we can conclude:
- In one half-life, \( \frac{N_0}{2} \) nuclei decay.
- In one average life, more than \( \frac{N_0}{2} \) nuclei decay.

Thus, the assertion is incorrect because it states that more nuclei decay in one half-life than in one average life.

### Final Answer
- **Assertion**: False
- **Reason**: True
- Therefore, the correct conclusion is that the assertion is false, but the reason is true.