Assertion Two different radioactive substances have initially same number of nuclei. Their decay constants are `lamda_(1)and lamda_(2)(ltlamda_(1)).` Then, initially first radioactiv substance decays at faster rate.
Reason Half-life of first radioactive substance is less.

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 reason provided regarding two different radioactive substances with the same initial number of nuclei but different decay constants.

### Step-by-Step Solution:

1. **Understanding Decay Rate**:
- The decay rate of a radioactive substance is given by the formula:
\[ R = \lambda N \]
where \( R \) is the decay rate, \( \lambda \) is the decay constant, and \( N \) is the number of nuclei present.

2. **Given Information**:
- We have two substances with decay constants \( \lambda_1 \) and \( \lambda_2 \) such that \( \lambda_1 > \lambda_2 \).
- Both substances start with the same number of nuclei, \( N_0 \).

3. **Comparing Decay Rates**:
- For the first substance (with decay constant \( \lambda_1 \)):
\[ R_1 = \lambda_1 N_0 \]
- For the second substance (with decay constant \( \lambda_2 \)):
\[ R_2 = \lambda_2 N_0 \]
- Since \( \lambda_1 > \lambda_2 \), it follows that:
\[ R_1 > R_2 \]
- Therefore, the first radioactive substance decays at a faster rate than the second.

4. **Understanding Half-life**:
- The half-life \( T_{1/2} \) of a radioactive substance is related to its decay constant by the formula:
\[ T_{1/2} = \frac{\ln 2}{\lambda} \]
- For the first substance:
\[ T_{1/2,1} = \frac{\ln 2}{\lambda_1} \]
- For the second substance:
\[ T_{1/2,2} = \frac{\ln 2}{\lambda_2} \]
- Since \( \lambda_1 > \lambda_2 \), it follows that:
\[ T_{1/2,1} < T_{1/2,2} \]
- This means the half-life of the first substance is less than that of the second.

5. **Conclusion**:
- The assertion states that the first radioactive substance decays at a faster rate, which is true.
- The reason states that the half-life of the first substance is less, which is also true.
- Since the reason correctly explains the assertion, both the assertion and reason are true.

### Final Answer:
Both the assertion and reason are true, and the reason is the correct explanation for the assertion.

---