Questions: The Strong Nuclear Force

Question 1

As a nucleus grows from A = 10 to A = 200, the binding energy per nucleon (B/A) roughly:

• A. Increases proportionally with A, because more nucleons means more bonds
• B. Decreases sharply, because proton repulsion grows faster than binding energy
• C. Stays roughly constant, peaking near iron at ~8.8 MeV/nucleon
• D. Oscillates depending on whether A is even or odd

Answer: (C)

B/A saturates near 8.8 MeV/nucleon rather than growing with A, because the strong force is short-range — each nucleon binds only to its immediate neighbors, not to every other nucleon in the nucleus. If the force were long-range like gravity, B/A would grow with A, but it doesn't. This saturation is direct evidence of the short-range character of the strong force and explains why nuclei have well-defined, roughly constant density cores.

Question 2

A proton on the far side of a large nucleus (e.g., uranium, A ≈ 238) relative to another proton. Which statement best describes their interaction?

• A. They interact via both the strong force and Coulomb repulsion equally
• B. They interact via Coulomb repulsion but not via the strong force
• C. They interact via the strong force but not Coulomb repulsion, since protons cancel
• D. They interact via neither force at nuclear distances

Answer: (B)

The strong force is effective only at ranges of ~2–3 fm, so nucleons on opposite sides of a large nucleus (separated by ~15 fm for uranium) do not feel each other's strong-force pull. However, the Coulomb (electrostatic) repulsion between protons is long-range (falls off as 1/r²) and is felt across the entire nucleus. This imbalance — every proton repels every other proton, but strong binding is only local — is why very heavy nuclei become increasingly unstable.

Question 3

The strong nuclear force acts with nearly equal strength between proton-proton, proton-neutron, and neutron-neutron pairs.

• T. True
• F. False

Answer: True

This property is called charge independence (or isospin symmetry). Experimental data from scattering experiments shows that the strong force does not distinguish between protons and neutrons — both are treated as nucleons differing only in their charge state. This symmetry is a deep hint that protons and neutrons are two faces of the same underlying particle, explained in the modern quark picture by the fact that the residual strong force between nucleons arises from quark-level color interactions that don't 'see' electric charge.

Question 4

Because the strong force is the most powerful known force, large nuclei are more tightly bound per nucleon than small ones.

• T. True
• F. False

Answer: False

The strength of the strong force does not translate into higher binding energy per nucleon for larger nuclei, because of saturation. Each nucleon binds only to its immediate neighbors (short range), so adding more nucleons adds more bonds proportionally — B/A stays roughly flat. In fact, for very large nuclei (beyond iron), B/A actually decreases slightly because Coulomb repulsion from the growing number of protons cannot be offset by the short-range strong force acting only locally. The 'most powerful force' claim applies at very short range; its short-range character is precisely what limits binding energy growth.

Question 5

Explain why saturation of binding energy per nucleon is direct evidence that the strong nuclear force has short range, rather than being a long-range force like gravity.

Model answer: If the strong force were long-range, each new nucleon added to a nucleus would bind to all existing nucleons, so total binding energy would scale as A² (number of pairs) and B/A would grow proportionally with A. Instead, B/A saturates near 8.8 MeV/nucleon because each nucleon only bonds to its nearest neighbors — adding a nucleon creates only a few new bonds regardless of how large the nucleus already is. Total binding energy thus scales linearly with A, giving constant B/A. Saturation is the macroscopic fingerprint of a short-range interaction.

This is the central reasoning chain that connects the observed nuclear data (flat B/A curve) to the microscopic property of the strong force (short range). Students who only memorize 'the strong force is short-range' without understanding how saturation proves it are missing the key insight.