Physics • Year 12 • Module 8 • Lesson 14
The Strong Nuclear Force
Apply the mass-defect and binding-energy relationships to real nuclear data, and reason quantitatively about nuclear stability and energy release.
1. Interpret nuclear binding-energy data
The table below lists nuclear masses for selected nuclides. Use the given data to answer all parts. Given: mp = 1.007276 u; mn = 1.008665 u; 1 u = 931.5 MeV/c². 10 marks
| Nuclide | Z (protons) | N (neutrons) | Nuclear mass (u) | Δm (u) | Eb (MeV) | Eb/A (MeV) |
|---|---|---|---|---|---|---|
| Helium-4 (4He) | 2 | 2 | 4.001506 | |||
| Carbon-12 (12C) | 6 | 6 | 11.996709 | |||
| Iron-56 (56Fe) | 26 | 30 | 55.920673 | |||
| Uranium-238 (238U) | 92 | 146 | 237.999922 |
Nuclear masses from AME2020 (rounded). Use mp = 1.007276 u, mn = 1.008665 u.
1.1 Complete the Δm, Eb, and Eb/A columns. Show full working for helium-4 in the space below. 6 marks (1.5 per row)
1.2 Which of the four nuclides in the table is the most stable? Justify your answer using the data you calculated. 2 marks
1.3 Based on the trend in your calculated Eb/A values, predict whether uranium-238 would tend to release energy by fission or by fusion. Justify your answer. 2 marks
2. Interpret the binding-energy-per-nucleon curve
The graph below shows the binding energy per nucleon (MeV) plotted against mass number (A) for representative nuclei. Use the graph to answer the questions. 7 marks
Figure 2. Schematic binding energy per nucleon curve for hydrogen through uranium. Data approximate; illustrative only.
2.1 Identify the nucleus with the highest binding energy per nucleon from the graph and state its approximate value. 2 marks
2.2 Using the graph, explain why both fusion of light nuclei and fission of heavy nuclei can release energy. Identify on the graph which region of the curve corresponds to each process. 3 marks
2.3 Explain why the binding energy per nucleon decreases for very heavy nuclei. What force is responsible? 2 marks
3. Compare the strong nuclear force and the Coulomb (electromagnetic) force
Complete the table below by filling in the missing cells. 8 marks (1 per cell)
| Property | Strong nuclear force | Coulomb (electromagnetic) force |
|---|---|---|
| Range | ||
| Particles affected | ||
| Charge dependence | ||
| Effect at very short distances (<0.5 fm) | ||
| Saturates with nucleon number? | ||
| Relative strength at nuclear distances | ||
| Exchange particle | ||
| Dominant in heavy nuclei (A > 200)? |
4. Predict and justify — nuclear stability scenario
Consider two hypothetical nuclei: nucleus X has A = 8, Z = 4 (beryllium-8); nucleus Y has A = 240, Z = 94 (plutonium-240). Use the binding energy per nucleon concept to answer the following. 5 marks
4.1 Predict whether nucleus X (Be-8) is likely to be stable or unstable, using the trend in the binding-energy curve for very light nuclei. Justify your prediction. 2 marks
4.2 Predict whether nucleus Y (Pu-240) would tend to release energy by fission or by fusion. Justify your answer by referring to the binding-energy curve. 2 marks
4.3 State the physical reason why nuclear reactions that increase the binding energy per nucleon of the products release energy. 1 mark
Q1.1 — Completed table
He-4: Δm = 2(1.007276) + 2(1.008665) − 4.001506 = 2.014552 + 2.017330 − 4.001506 = 0.030376 u. Eb = 0.030376 × 931.5 = 28.30 MeV. Eb/A = 28.30/4 = 7.07 MeV. [Full working shown — award marks here]
C-12: Δm = 6(1.007276) + 6(1.008665) − 11.996709 = 6.043656 + 6.051990 − 11.996709 = 0.098937 u. Eb = 0.098937 × 931.5 = 92.16 MeV. Eb/A = 92.16/12 = 7.68 MeV.
Fe-56: Δm = 26(1.007276) + 30(1.008665) − 55.920673 = 26.189176 + 30.259950 − 55.920673 = 0.528453 u. Eb = 0.528453 × 931.5 = 492.26 MeV. Eb/A = 492.26/56 = 8.79 MeV.
U-238: Δm = 92(1.007276) + 146(1.008665) − 237.999922 = 92.669392 + 147.265090 − 237.999922 = 1.934560 u. Eb = 1.934560 × 931.5 = 1802.0 MeV. Eb/A = 1802.0/238 = 7.57 MeV.
Q1.2 — Most stable nuclide (2 marks)
Iron-56 is the most stable, with the highest binding energy per nucleon (~8.79 MeV/nucleon) [1]. A higher binding energy per nucleon means nucleons are more tightly bound and more energy would be required to disassemble the nucleus [1].
Q1.3 — Fission or fusion for uranium (2 marks)
Uranium-238 has Eb/A ≈ 7.57 MeV, which is less than that of iron-56. It lies on the right (heavy nucleus) side of the binding-energy curve [1]. Splitting it by fission would produce lighter fragments with higher Eb/A, releasing the difference in binding energy as kinetic energy [1].
Q2.1 — Highest Eb/A (2 marks)
Iron-56 (56Fe), with a binding energy per nucleon of approximately 8.8 MeV [1 each].
Q2.2 — Fusion and fission from the graph (3 marks)
Energy is released in any nuclear reaction where the products have a higher binding energy per nucleon than the reactants [1]. For fusion: light nuclei (left side of the curve, A < 56) have lower Eb/A. Combining them produces a nucleus closer to iron-56 with higher Eb/A; the difference in binding energy is released [1]. For fission: heavy nuclei (right side of the curve, A > 56) have lower Eb/A. Splitting them produces two medium-mass fragments with higher Eb/A; again the difference is released [1].
Q2.3 — Why Eb/A decreases for heavy nuclei (2 marks)
As Z increases in very heavy nuclei, Coulomb repulsion between protons accumulates [1]. The strong force is short-range and saturates (each nucleon only interacts with its immediate neighbours), so additional protons add Coulomb repulsion but contribute less binding. This reduces the average binding energy per nucleon [1].
Q3 — Comparison table
Range: Strong: ~1–3 fm; Coulomb: infinite. Particles affected: Strong: all nucleons (p–p, n–n, p–n); Coulomb: charged particles only (protons repel each other). Charge dependence: Strong: charge-independent; Coulomb: depends on charge. At <0.5 fm: Strong: repulsive; Coulomb: strongly repulsive. Saturates: Strong: yes (only nearest neighbours); Coulomb: no (acts between all proton pairs). Relative strength: Strong: ~100× stronger than Coulomb at nuclear distances; Coulomb: weaker at fm scale. Exchange particle: Strong: gluon (QCD) / pion (Yukawa); Coulomb: photon. Dominant in heavy nuclei: Strong: no (Coulomb wins); Coulomb: yes.
Q4.1 — Beryllium-8 stability (2 marks)
Beryllium-8 (A = 8) lies on the steeply rising, left-hand part of the binding-energy curve, where Eb/A is still relatively low. Be-8 actually has a very low binding energy per nucleon (approximately 7.06 MeV) and is known to be unstable, spontaneously splitting into two helium-4 nuclei [1]. This is because two separate alpha particles have slightly higher binding energy per nucleon than Be-8, so the decay is energetically favourable [1].
Q4.2 — Plutonium-240: fission or fusion (2 marks)
Plutonium-240 (A = 240, Z = 94) is a very heavy nucleus lying on the right-hand, decreasing side of the binding-energy curve [1]. Fission would split it into two medium-mass fragments with higher Eb/A, releasing energy; this is energetically favoured over fusion, which would move it even further from the iron-56 peak [1].
Q4.3 — Why higher Eb/A releases energy (1 mark)
The mass defect — and hence the binding energy — of the products is greater than that of the reactants. By mass–energy equivalence (E = mc²), this extra binding energy comes from a reduction in mass, which is released as kinetic energy of the products [1].