For a stable nuclei the

Options

A. Biding energy is large
B. Binding energy per nucleons is large
C. Packing fraction is very large
D. Packing fraction is very small

Answer

To determine the correct options for the stability of a nucleus, we need to analyze the concepts of binding energy and packing fraction.

### Step-by-Step Solution:

1. **Understanding Binding Energy**:
- Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. A higher binding energy indicates a more stable nucleus.
- The binding energy can also be related to the mass defect, which is the difference between the mass of the nucleus and the sum of the individual masses of its protons and neutrons.

**Hint**: Remember that a larger binding energy means the nucleus is more stable.

2. **Binding Energy per Nucleon**:
- Binding energy per nucleon is calculated by dividing the total binding energy by the number of nucleons (protons + neutrons). This value helps compare the stability of different nuclei.
- For stable nuclei, the binding energy per nucleon is generally large, especially for intermediate mass nuclei (like Iron).

**Hint**: Look for the trend in binding energy per nucleon across different elements; it peaks for intermediate mass elements.

3. **Understanding Packing Fraction**:
- The packing fraction is defined as the ratio of the mass defect to the mass number of the nucleus. It indicates how tightly packed the nucleons are within the nucleus.
- A positive packing fraction suggests that the isotopic mass is greater than the mass number, while a negative packing fraction indicates the opposite.

**Hint**: A smaller packing fraction (or a negative value) typically indicates a more stable nucleus.

4. **Evaluating the Options**:
- **Option A**: Binding energy is large - This is true for stable nuclei.
- **Option B**: Binding energy per nucleon is large - This is also true for stable nuclei.
- **Option C**: Packing fraction is very large - This is not generally true for stable nuclei.
- **Option D**: Packing fraction is very small - This is true for stable nuclei.

5. **Conclusion**:
- The correct options for a stable nucleus are **B** (binding energy per nucleon is large) and **D** (packing fraction is very small).

### Final Answer:
The correct options for a stable nucleus are **B and D**.