Assertion: `""_(Z)X^(A)` undergoes `2alpha`- decays, `2beta-` decays and `2gamma`- decays and the daughter product is `""_(Z- 2)Y^(A- 8)`
Reason : In `alpha`- decay the mass number decreases by 4 and atomic number decreases by 2. In `beta`- decay the mass number remains unchanged, but atomic number increases by 1 only

Options

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

Explanation

To solve the given problem, we need to analyze the assertion and the reason provided in the question step by step.

### Step 1: Understanding the Assertion
The assertion states that the nuclide \(_{Z}X^{A}\) undergoes 2 alpha decays, 2 beta minus decays, and 2 gamma decays, resulting in the daughter product \(_{Z-2}Y^{A-8}\).

1. **Alpha Decay**: Each alpha decay decreases the atomic number (Z) by 2 and the mass number (A) by 4.
- After 1 alpha decay: \(_{Z}X^{A} \rightarrow _{Z-2}X^{A-4}\)
- After 2 alpha decays: \(_{Z-2}X^{A-4} \rightarrow _{Z-4}X^{A-8}\)

2. **Beta Minus Decay**: Each beta minus decay does not change the mass number (A) but increases the atomic number (Z) by 1.
- After 1 beta minus decay: \(_{Z-4}X^{A-8} \rightarrow _{Z-3}X^{A-8}\)
- After 2 beta minus decays: \(_{Z-3}X^{A-8} \rightarrow _{Z-2}X^{A-8}\)

3. **Gamma Decay**: Gamma decay does not change either the atomic number or the mass number.
- After 2 gamma decays: The nuclide remains \(_{Z-2}X^{A-8}\).

Thus, after all the decays, we end up with \(_{Z-2}X^{A-8}\), which can be represented as \(_{Z-2}Y^{A-8}\) (where Y is the new nuclide).

### Conclusion for Assertion
The assertion is true because the final daughter product after the specified decays is indeed \(_{Z-2}Y^{A-8}\).

### Step 2: Understanding the Reason
The reason states that in alpha decay, the mass number decreases by 4 and the atomic number decreases by 2, and in beta minus decay, the mass number remains unchanged while the atomic number increases by 1.

- This statement is correct for both types of decay:
- **Alpha Decay**: Mass number decreases by 4, atomic number decreases by 2.
- **Beta Minus Decay**: Mass number remains the same, atomic number increases by 1.

### Conclusion for Reason
The reason is also true and correctly explains the changes occurring during the alpha and beta decays.

### Final Conclusion
Both the assertion and the reason are true, and the reason provides a correct explanation for the assertion.

### Answer
The correct option is: **Both assertion and reason are true, and the reason is the correct explanation of the assertion.**

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