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

Options

A. If both (A) and (R ) are correct, and (R ) is the correct explanation of (A).
B. If both (A) and (R ) are correct, but (R ) is not the correct explanation of (A)
C. If (A) is correct, but (R ) is incorrect.
D. If (A) is incorrect, but (R ) is correct

Explanation

To analyze the assertion and reason provided in the question, we will break down the steps involved in determining the stability of the nuclides mentioned.

### Step-by-Step Solution:

1. **Identify the Nuclides**:
- The assertion states that the nuclide Aluminium-30 (Al-30) is less stable than Calcium-40 (Ca-40).
- Al-30 has an atomic number of 13 and a mass number of 30.
- Ca-40 has an atomic number of 20 and a mass number of 40.

2. **Calculate the Number of Protons and Neutrons**:
- For Al-30:
- Number of protons (Z) = 13 (from the atomic number).
- Number of neutrons (N) = Mass number - Atomic number = 30 - 13 = 17.
- For Ca-40:
- Number of protons (Z) = 20 (from the atomic number).
- Number of neutrons (N) = Mass number - Atomic number = 40 - 20 = 20.

3. **Calculate the Neutron-to-Proton Ratio (N/P Ratio)**:
- For Al-30:
- N/P Ratio = Number of neutrons / Number of protons = 17 / 13 ≈ 1.31.
- For Ca-40:
- N/P Ratio = Number of neutrons / Number of protons = 20 / 20 = 1.

4. **Analyze Stability Based on N/P Ratio**:
- A nuclide is generally considered unstable if its N/P ratio is significantly greater than 1.
- For Al-30, the N/P ratio is approximately 1.31, which indicates instability.
- For Ca-40, the N/P ratio is exactly 1, which suggests stability.

5. **Evaluate the Assertion**:
- The assertion states that Al-30 is less stable than Ca-40. Based on our calculations, this is true since Al-30 has a higher N/P ratio indicating it is less stable.

6. **Evaluate the Reason**:
- The reason states that nuclides with an odd number of protons and neutrons are generally unstable.
- Al-30 has 13 protons (odd) and 17 neutrons (odd), which supports the reason.
- Ca-40 has an even number of protons (20) and neutrons (20), which aligns with the stability observed.

7. **Conclusion**:
- Both the assertion and the reason are correct, and the reason correctly explains the assertion.

### Final Answer:
Both Assertion (A) and Reason (R) are correct, and R is the correct explanation of A.