The compound unstabel nucleus `._(92)^(236)U` often decays in accordance with the following reaction
`._(92)^(236)U rarr ._(54)^(140)Xe +._(38)^(94)Sr ` + other particles
During the reaction, the uranium nucleus ''fissions'' (splits) into the two smaller nuceli have higher nuclear binding energy per nucleon (although the lighter nuclei have lower total nuclear binding energies, because they contain fewer nucleons).
Inside a nucleus, the nucleons (protons and neutrons)attract each other with a ''strong nuclear'' force. All neutrons exert approxiamtely the same strong nuclear force on each other. This force holds the nuclear are very close together at intranuclear distances.
Why is a `._2^4He` nucleus more stable than a `._3^4Li` nucleus?

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 contaning more protons than neutrons.
C. Forces other than the strong nuclear force make the lithium nulceus less stable.
D. none of these

Explanation

To determine why the helium nucleus \( _{2}^{4}\text{He} \) is more stable than the lithium nucleus \( _{3}^{4}\text{Li} \), we can analyze the composition and forces acting within each nucleus.

### Step-by-Step Solution:

1. **Identify the Composition of Each Nucleus**:
- The helium nucleus \( _{2}^{4}\text{He} \) consists of 2 protons and 2 neutrons.
- The lithium nucleus \( _{3}^{4}\text{Li} \) consists of 3 protons and 1 neutron.

2. **Understand the Forces at Play**:
- Inside a nucleus, nucleons (protons and neutrons) attract each other through the strong nuclear force, which is very powerful but acts over a short range.
- Protons, being positively charged, repel each other due to electrostatic force. This repulsion increases with the number of protons.

3. **Calculate the Neutron-to-Proton Ratio**:
- For helium: Neutron-to-proton ratio = \( \frac{2}{2} = 1 \)
- For lithium: Neutron-to-proton ratio = \( \frac{1}{3} \approx 0.33 \)

4. **Analyze the Stability**:
- In helium, the strong nuclear force is sufficient to hold the nucleus together because the number of neutrons is equal to the number of protons, effectively balancing the repulsive forces.
- In lithium, the presence of 3 protons leads to significant electrostatic repulsion, which can overcome the strong nuclear force. The single neutron does not provide enough binding to stabilize the nucleus against this repulsion.

5. **Conclusion**:
- The helium nucleus \( _{2}^{4}\text{He} \) is more stable than the lithium nucleus \( _{3}^{4}\text{Li} \) because it has a balanced neutron-to-proton ratio, allowing the strong nuclear force to dominate over the electrostatic repulsion. In contrast, the lithium nucleus has a higher proton count, leading to greater repulsion and less stability.

### Final Answer:
The helium nucleus \( _{2}^{4}\text{He} \) is more stable than the lithium nucleus \( _{3}^{4}\text{Li} \) due to its balanced neutron-to-proton ratio, which allows the strong nuclear force to effectively counteract the electrostatic repulsion between protons.