We have two nuclei `""_(4)X^(8)` and `""_(5)Y^(9)` .

Options

A. Nuclei X is more stable than Y.
B. The stability of both X and Y is equal
C. Nuclei Y is more stable than X.
D. Nothing can be said.

Explanation

To determine which of the two nuclei, \( _{4}X^{8} \) and \( _{5}Y^{9} \), is more stable, we will analyze the neutron-to-proton ratio for each nucleus. The stability of a nucleus is often assessed by this ratio, where a ratio close to 1 indicates greater stability.

### Step-by-Step Solution:

1. **Identify the atomic numbers and mass numbers:**
- For nucleus \( X \):
- Atomic number (Z) = 4
- Atomic mass (A) = 8
- For nucleus \( Y \):
- Atomic number (Z) = 5
- Atomic mass (A) = 9

2. **Calculate the number of protons and neutrons for each nucleus:**
- For nucleus \( X \):
- Number of protons (P) = Atomic number = 4
- Number of neutrons (N) = Atomic mass - Atomic number = 8 - 4 = 4
- For nucleus \( Y \):
- Number of protons (P) = Atomic number = 5
- Number of neutrons (N) = Atomic mass - Atomic number = 9 - 5 = 4

3. **Calculate the neutron-to-proton ratio (N/P) for each nucleus:**
- For nucleus \( X \):
- Neutron-to-proton ratio \( \frac{N}{P} = \frac{4}{4} = 1 \)
- For nucleus \( Y \):
- Neutron-to-proton ratio \( \frac{N}{P} = \frac{4}{5} = 0.8 \)

4. **Compare the neutron-to-proton ratios:**
- The ratio for nucleus \( X \) is 1, while the ratio for nucleus \( Y \) is 0.8.
- A ratio of 1 indicates a more stable nucleus compared to a ratio of 0.8.

5. **Conclusion:**
- Since the neutron-to-proton ratio for nucleus \( X \) is equal to 1, and for nucleus \( Y \) it is 0.8, we conclude that nucleus \( X \) is more stable than nucleus \( Y \).

### Final Answer:
Nucleus \( _{4}X^{8} \) is more stable than nucleus \( _{5}Y^{9} \).

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