Q.8 The “strong nuclear force” holds the protons and neutrons (nucleons) together in the nucleus of an
atom. It is found that the binding energy per nucleon (for the nucleus of an element) when plotted
against the mass number (A) of that element changes very little for 30 < A < 150. The binding
energy is lower for A << 30 or A >> 150. This leads us to conclude that
(A) the strong nuclear force must oscillate with distance with a periodicity approximately same as
the size of a proton or neutron
(B) the fusion of two elements, both with A << 30 or fission of an element A >> 150 may release
energy
(C) the strong nuclear force changes very slowly with distance (i.e. It is long ranged on the scale of
the size of nucleus)
(D) the strong nuclear force goes to zero very rapidly with distance (i.e. It is short ranged on the
scale of the size of nucleus)
The correct answer is (D).
The binding energy per nucleon remains nearly constant for mass numbers 30 < A < 150 due to the short-range nature of the strong nuclear force, which saturates as each nucleon interacts only with its nearest neighbors.
Option Analysis
(A) Incorrect. The strong nuclear force does not oscillate with a periodicity matching proton or neutron size (~1 fm); it shows repulsive behavior below 0.5 fm and attractive up to ~3 fm without periodic oscillation.
(B) Partially correct but incomplete. Fusion of light nuclei (A << 30) and fission of heavy nuclei (A >> 150) release energy as products have higher binding energy per nucleon, but this follows from the curve’s shape rather than directly concluding the force’s nature.
(C) Incorrect. A long-range force would maintain high binding energy across all A values without drop-off; the observed plateau and decreases indicate limited range on nuclear scales (~few fm).
(D) Correct. The force’s short range (~1-3 fm, comparable to nucleon separation) causes saturation: interior nucleons bind equally regardless of nucleus size, keeping binding energy per nucleon constant until Coulomb repulsion dominates in heavy nuclei.
The binding energy per nucleon curve reveals key insights into nuclear stability and the strong nuclear force range. For nuclei with mass numbers between 30 and 150, this curve shows a broad plateau where binding energy per nucleon remains nearly constant at ~8 MeV, peaking near iron-56.
Curve Features
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Light nuclei (A << 30): Low binding energy; fusion to heavier nuclei increases average binding, releasing energy.
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Medium nuclei (30 < A < 150): Saturation effect yields stable binding per nucleon.
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Heavy nuclei (A >> 150): Decreasing trend due to rising Coulomb repulsion overpowering short-range attraction.
Strong Nuclear Force Role
The strong nuclear force operates over ~1-3 fm, matching nucleon spacing (~1 fm separation). This short range ensures each nucleon binds only nearest neighbors, explaining the plateau: adding nucleons does not proportionally increase total binding beyond local interactions.
In larger nuclei, long-range electromagnetic repulsion between protons reduces net binding, leading to instability and fission potential. Light nuclei gain stability via fusion as strong force dominates without excess repulsion.
