Physics • Year 12 • Module 8 • Lesson 14
The Strong Nuclear Force
Build HSC Band 5–6 extended-response technique on binding-energy calculations, nuclear stability analysis, and the evaluation of fusion vs fission as energy sources.
1. Multi-step calculation — binding energy of carbon-12 (Band 5–6)
8 marks Band 5–6
Given data: mp = 1.007276 u; mn = 1.008665 u; mC-12 = 12.000000 u; 1 u = 931.5 MeV/c²; 1 MeV = 1.602 × 10−13 J; c = 3.00 × 108 m s−1.
Q1. Carbon-12 (12C) has 6 protons and 6 neutrons. Answer each part below.
(a) Calculate the mass defect (Δm) for carbon-12 in unified atomic mass units (u). (2 marks)
(b) Calculate the binding energy of carbon-12 in MeV. (1 mark)
(c) Calculate the binding energy per nucleon for carbon-12 in MeV/nucleon. (1 mark)
(d) Convert the total binding energy of carbon-12 to joules. (1 mark)
(e) Compare your result in (c) to the value for iron-56 (~8.79 MeV/nucleon) and helium-4 (~7.07 MeV/nucleon). State what this comparison tells you about the relative stability of carbon-12. (2 marks)
(f) In stellar nucleosynthesis, three helium-4 nuclei fuse to form one carbon-12 nucleus. Using your calculated binding energies, determine whether this triple-alpha fusion reaction releases or absorbs energy. Calculate the energy released or absorbed in MeV. (1 mark)
2. Data + scenario: evaluating fusion and fission as energy sources (Band 5–6)
8 marks Band 5–6
Scenario. Engineers designing next-generation power plants consider two nuclear reactions. Reaction 1 (fusion): two deuterium nuclei (2H, Eb/A ≈ 1.11 MeV) combine to form helium-4 (4He, Eb/A ≈ 7.07 MeV). Reaction 2 (fission): uranium-235 (235U, Eb/A ≈ 7.59 MeV) absorbs a neutron and splits into krypton-92 (92Kr, Eb/A ≈ 8.72 MeV) and barium-141 (141Ba, Eb/A ≈ 8.36 MeV) plus three neutrons. The table below summarises the comparison.
| Criterion | Fusion (D–D) | Fission (U-235) |
|---|---|---|
| Eb/A of reactants (MeV) | ~1.11 (deuterium) | ~7.59 (U-235) |
| Eb/A of products (MeV) | ~7.07 (He-4) | ~8.5 (average of Kr-92, Ba-141) |
| Energy released per reaction (approx.) | ~24 MeV | ~200 MeV |
| Energy per kg of fuel | Very high (~3×1014 J/kg) | High (~8×1013 J/kg) |
| Fuel availability | Deuterium abundant in seawater | U-235 rare (0.7% of natural uranium) |
| Radioactive waste | Minimal (helium product) | Long-lived fission products |
| Technical readiness | Not yet commercially viable | Operational since 1950s |
Q2. Analyse and evaluate the data and the strong-force model to address the following. In your response you must:
- Explain, using the binding-energy-per-nucleon concept, why both reactions release energy.
- Explain the role of the strong nuclear force in enabling these reactions to release energy.
- Identify which reaction releases more energy per kilogram of fuel and explain why in terms of binding energy changes.
- Evaluate one advantage and one disadvantage of each reaction as a practical energy source.
- Reach a justified conclusion about which energy source is more promising for the long term, based on the data.
Q1(a) — Mass defect (2 marks)
Δm = 6(1.007276) + 6(1.008665) − 12.000000 = 6.043656 + 6.051990 − 12.000000 = 0.098646 u [1 for working, 1 for correct value]. Note: accept 0.09865 u for rounding.
Q1(b) — Binding energy in MeV (1 mark)
Eb = 0.098646 × 931.5 = 91.9 MeV [1]. (Accept 92.2 MeV if Δm = 0.09896 u used.)
Q1(c) — Binding energy per nucleon (1 mark)
Eb/A = 91.9/12 = 7.66 MeV/nucleon [1].
Q1(d) — Binding energy in joules (1 mark)
Eb = 91.9 × 1.602 × 10−13 = 1.47 × 10−11 J [1].
Q1(e) — Comparison with He-4 and Fe-56 (2 marks)
Carbon-12 (Eb/A ≈ 7.66 MeV/nucleon) is more stable than helium-4 (7.07 MeV/nucleon) but less stable than iron-56 (8.79 MeV/nucleon) [1]. This means carbon-12 lies on the rising part of the binding-energy curve between very light nuclei and the most stable region; it could in principle release energy by fusing to form heavier nuclei up to iron-56 [1].
Q1(f) — Triple-alpha fusion energy (1 mark)
Eb(C-12) ≈ 91.9 MeV; 3 × Eb(He-4) ≈ 3 × 28.30 = 84.9 MeV. Energy released = 91.9 − 84.9 = 7.0 MeV [1]. Since the products have greater total binding energy than the reactants, energy is released. (The actual value is ~7.27 MeV, consistent with a small rounding range.)
Q2 — Sample Band 6 response (8 marks)
Why both reactions release energy: In both reactions the products have a higher binding energy per nucleon than the reactants. Fusion: deuterium has Eb/A ≈ 1.11 MeV but helium-4 has ≈ 7.07 MeV — a gain of about 6 MeV/nucleon. Fission: uranium-235 has Eb/A ≈ 7.59 MeV but the fragments average ≈ 8.5 MeV — a gain of about 0.9 MeV/nucleon. In both cases the products are more tightly bound; the extra binding energy is released as kinetic energy of the products, corresponding to a loss of mass via E = Δmc² [1 mark — both reactions explained with Eb/A data cited].
Role of the strong nuclear force: The strong nuclear force holds nucleons together inside the nucleus, creating the binding energy in the first place. The energy released in fusion and fission comes from the fact that the strong force creates a greater total binding energy in the products than in the reactants. The difference is the energy released. Without the strong force, there would be no nuclear binding energy and no energy source in these reactions [1 mark].
Energy per kilogram: Fusion releases more energy per kilogram (~3×1014 J/kg vs ~8×1013 J/kg). This is because deuterium nuclei are very light (A=2) and the gain in Eb/A per nucleon (~6 MeV) is very large relative to the nucleon mass. Fission releases more energy per reaction (~200 MeV vs ~24 MeV for D–D), but uranium-235 is 117.5 times heavier than deuterium, making the energy density lower per unit mass [1 mark — correctly identifies fusion as higher E/kg with reasoning].
Advantage / disadvantage of fusion: Advantage: abundant fuel (deuterium from seawater) and minimal radioactive waste. Disadvantage: not yet commercially viable; enormous technical challenges in achieving the temperatures and pressures needed for sustained plasma confinement [1 mark each for valid advantage and disadvantage].
Advantage / disadvantage of fission: Advantage: proven commercial technology operating since the 1950s. Disadvantage: limited U-235 supply and long-lived radioactive waste requiring secure storage for thousands of years [1 mark each for valid advantage and disadvantage].
Conclusion: Based on the data, fusion is the more promising long-term energy source because of its far greater energy density, vastly more abundant fuel, and negligible radioactive waste. However, it cannot currently be regarded as a practical energy source. Fission is the viable near-term option. A balanced answer might conclude that both will likely coexist, with fission serving as a bridge technology until fusion is commercially realised [1 mark for an explicit, evidence-based judgement].
Marking criteria (8 marks): 1 = explains why both reactions release energy using Eb/A increases; 1 = explains role of strong force in creating binding energy; 1 = identifies fusion as higher energy/kg with correct reasoning; 1 = fusion advantage; 1 = fusion disadvantage; 1 = fission advantage; 1 = fission disadvantage; 1 = explicit evidence-based conclusion.