Assertion (A) : Nuclide `AI_(13)^(30)` is less stable than `Ca_(20)^(40)`
Reason (R ) : Nuclide having unequal number of proton and neutrons are generally unstable

Options

A. If both (A) and (R ) correct and (R ) is the correct explanation for (A)
B. If both (A) and (R ) correct and (R ) is the correct explanation for (A)
C. If (A) is correct but (R ) is incorrect
D. If (A) is incorrect but (R ) is correct

Explanation

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

### Step 1: Analyze the Assertion
The assertion states that the nuclide \( \text{Al}_{13}^{30} \) is less stable than \( \text{Ca}_{20}^{40} \).

1. **Identify the number of protons and neutrons:**
- For \( \text{Al}_{13}^{30} \):
- Protons (Z) = 13
- Neutrons (N) = 30 - 13 = 17
- For \( \text{Ca}_{20}^{40} \):
- Protons (Z) = 20
- Neutrons (N) = 40 - 20 = 20

2. **Calculate the neutron-to-proton ratio (N/Z):**
- For \( \text{Al}_{13}^{30} \):
- \( \frac{N}{Z} = \frac{17}{13} \approx 1.31 \)
- For \( \text{Ca}_{20}^{40} \):
- \( \frac{N}{Z} = \frac{20}{20} = 1.0 \)

3. **Determine stability based on the N/Z ratio:**
- A ratio closer to 1 indicates greater stability. Since \( \text{Ca}_{20}^{40} \) has an N/Z ratio of 1.0, it is more stable than \( \text{Al}_{13}^{30} \) which has a ratio of approximately 1.31.

### Conclusion for Assertion
The assertion is correct: \( \text{Al}_{13}^{30} \) is indeed less stable than \( \text{Ca}_{20}^{40} \).

### Step 2: Analyze the Reason
The reason states that nuclides having unequal numbers of protons and neutrons are generally unstable.

1. **Understanding the statement:**
- Generally, stable nuclides have a balanced ratio of neutrons to protons. If the number of neutrons significantly deviates from the number of protons, the nuclide tends to be unstable.

### Conclusion for Reason
The reason is also correct: nuclides with unequal numbers of protons and neutrons are generally unstable.

### Final Conclusion
Both the assertion and reason are correct, and the reason provided is a valid explanation for the assertion.

### Answer
Both Assertion (A) and Reason (R) are correct, and R is the correct reason for A.

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