Nuclear Forces MCQ: Analyzing Nucleon Interactions

This section provides a detailed analysis of the multiple-choice question regarding the forces acting within an atomic nucleus, specifically focusing on electrostatic repulsion, nuclear force, gravitational force, and binding energy per nucleon.

Statement (A): Electrostatic Force vs. Nuclear Force

Statement (A) suggests that the electrostatic repulsive force between protons can exceed the nuclear force that binds nucleons. The strong nuclear force is the fundamental force responsible for holding protons and neutrons (collectively called nucleons) together within the atomic nucleus. It is an attractive force that operates over very short distances (approximately $10^{-15}$ meters). Protons, having positive charges, repel each other due to the electrostatic (Coulomb) force. While this repulsion exists, especially in larger nuclei, the strong nuclear force is significantly stronger at the nuclear scale, overcoming the electrostatic repulsion to maintain nuclear stability. If the electrostatic force were stronger than the nuclear force, nuclei would not be stable. Therefore, statement (A) is incorrect.

Statement (B): Forces in Smaller Nuclei

Statement (B) proposes that in smaller nuclei, the electrostatic repulsion between protons is much weaker than the nuclear force. This is correct. In smaller nuclei, there are fewer protons, which inherently reduces the total electrostatic repulsive force. Simultaneously, the nucleons are packed closely together, allowing the short-range, powerful nuclear force to dominate effectively. The nuclear force's strength far surpasses the electrostatic repulsion at these close proximity scales. Hence, statement (B) is accurate.

Statement (C): Gravitational Force vs. Nuclear Force

Statement (C) asserts that the gravitational force between nucleons is much smaller than the nuclear force. This is also correct. The gravitational force is dependent on mass. Nucleons, although having mass, are incredibly tiny, resulting in extremely weak gravitational attraction between them. The strong nuclear force is vastly stronger—by many orders of magnitude—than the gravitational force at the distances relevant within the nucleus. The electrostatic force also significantly outweighs gravity in this context. Therefore, statement (C) is accurate.

Statement (D): Binding Energy and Force Range

Statement (D) claims that the binding energy per nucleon is nearly constant because the nuclear force is long-range. The observation that binding energy per nucleon is approximately constant (around 8 MeV) for most stable nuclei is a crucial aspect of nuclear physics, related to the saturation of nuclear forces. However, this phenomenon occurs because the nuclear force is a short-range force. This means each nucleon interacts strongly only with its nearest neighbors, not with all other nucleons in the nucleus. This saturation limits the increase in binding energy per nucleon as the nucleus grows larger. If the nuclear force were long-range, the binding energy per nucleon would typically increase with the size of the nucleus. Thus, statement (D) is incorrect because it misidentifies the range of the nuclear force as the reason for the constant binding energy per nucleon.

Final Conclusion

After analyzing each statement, we find that statements (B) and (C) are correct. Therefore, the correct option is the one that includes only (B) and (C).