For a nucleus to be stable, the correct relation between neutron number `N` and proton number `Z` is.

Options

A. `NgtZ`
B. `N=Z`
C. `NltZ`
D. `NgeZ`

Answer

To determine the correct relation between the neutron number \( N \) and the proton number \( Z \) for a nucleus to be stable, we can analyze the behavior of lighter and heavier nuclei.

### Step-by-Step Solution:

1. **Understanding Lighter Nuclei:**
- For lighter nuclei (nuclei with a small mass number), the ratio of neutrons to protons is approximately 1. This means that the number of neutrons is equal to the number of protons.
- Mathematically, we can express this as:
\[ N \approx Z \]

2. **Understanding Heavier Nuclei:**
- For heavier nuclei (nuclei with a large mass number), stability requires that the number of neutrons exceeds the number of protons. This is due to the increasing repulsive forces between protons as the number of protons increases.
- For these nuclei, the ratio of neutrons to protons is greater than 1:
\[ N > Z \]

3. **Combining the Conditions:**
- From the above two points, we can summarize the conditions for stability:
- For lighter nuclei: \( N \approx Z \)
- For heavier nuclei: \( N > Z \)
- Combining these conditions, we can conclude that for a nucleus to be stable, the number of neutrons must be greater than or equal to the number of protons:
\[ N \geq Z \]

4. **Conclusion:**
- Therefore, the correct relation between the neutron number \( N \) and the proton number \( Z \) for a nucleus to be stable is:
\[ N \geq Z \]

### Final Answer:
The correct relation for a nucleus to be stable is \( N \geq Z \).

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