Why is a `._(2)^(4)He` nucleus more stable than a `._(3)^(4)Li` nucles ?

Options

A. The strong nuclear force is larger when the neutron to proton ratio is higher
B. The laws of nuclear physics forbid a nucleus from containing more protons than neutrons
C. Forces other than the strong nuclear force make the lithium nucleus less stable
D. None of the above

Answer

To determine why a \(_{2}^{4}\text{He}\) nucleus is more stable than a \(_{3}^{4}\text{Li}\) nucleus, we can analyze the neutron-to-proton ratio and the forces acting within the nucleus.

### Step-by-Step Solution:

1. **Identify the Composition of the Nuclei**:
- The \(_{2}^{4}\text{He}\) nucleus (Helium) has 2 protons and 2 neutrons.
- The \(_{3}^{4}\text{Li}\) nucleus (Lithium) has 3 protons and 1 neutron.

2. **Calculate the Neutron-to-Proton Ratio**:
- For Helium: Neutron-to-Proton Ratio = Number of Neutrons / Number of Protons = 2 / 2 = 1.
- For Lithium: Neutron-to-Proton Ratio = Number of Neutrons / Number of Protons = 1 / 3 ≈ 0.33.

3. **Analyze Stability Based on Neutron-to-Proton Ratio**:
- A neutron-to-proton ratio of 1 (like in Helium) is generally considered stable.
- A lower ratio (like in Lithium) suggests instability, as there are not enough neutrons to effectively counterbalance the electrostatic repulsion between the protons.

4. **Consider the Strong Nuclear Force**:
- The strong nuclear force binds protons and neutrons together in the nucleus. It is more effective when there are more neutrons present to help bind the protons.
- In Helium, the strong nuclear force is sufficient to overcome the repulsion between the 2 protons.
- In Lithium, the presence of 3 protons increases the electrostatic repulsion, which is not adequately countered by the single neutron.

5. **Electrostatic Repulsion**:
- In Helium, with only 2 protons, there is less electrostatic repulsion compared to Lithium, which has 3 protons.
- The increased repulsion in Lithium contributes to its instability.

6. **Conclusion**:
- The \(_{2}^{4}\text{He}\) nucleus is more stable than the \(_{3}^{4}\text{Li}\) nucleus due to a favorable neutron-to-proton ratio and a lower level of electrostatic repulsion.

### Final Answer:
The \(_{2}^{4}\text{He}\) nucleus is more stable than the \(_{3}^{4}\text{Li}\) nucleus because it has a neutron-to-proton ratio of 1, which is ideal for stability, while Lithium has a lower ratio of approximately 0.33, leading to greater instability due to increased electrostatic repulsion among protons.