The shape of the lesson
By the end of the lesson, learners can
- Climb toward iron: Slide along the binding-energy-per-nucleon curve.
- Mass, energy, and the curve: A few definitions and one constant carry the whole topic.
- Binding energy: Δm = Σ(nucleon masses) − M; binding energy = Δm c²; stability from BE per nucleon.
- Reaction energy: E = c²Δm with Δm = mass of reactants − mass of products.
- Decay: A = λN; N = N₀e⁻λᵗ; λ t½ = ln2; fraction after n half-lives = (½)ⁿ.
One picture every idea returns to
The mass defect Δm is the difference between the total mass of the separate nucleons and the smaller mass of the bound nucleus. By E = mc² this corresponds to the binding energy = Δm c²: the energy released when the nucleus forms, or needed to pull it apart. The binding energy per nucleon peaks near iron, so fusing light nuclei and splitting heavy nuclei both release energy.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, The mass that becomes energy.. A nucleus weighs less than the protons and neutrons that make it. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Climb toward iron | Slide along the binding-energy-per-nucleon curve. Project tab 1 of the lab (Mass defect and binding energy) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Mass, energy, and the curve | A few definitions and one constant carry the whole topic. | Corners |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 48 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Mass, energy, and the curve, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Corners
Put one answer or viewpoint in each corner of the room. Students move to the corner they agree with, justify the choice to a partner there, then hear one voice from each corner before the reveal.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Stability is measured by binding energy per nucleon, not total binding energy (uranium has the largest total but is far less stable than iron). | For the energy released in a reaction, use E = c²Δm with Δm = (mass of reactants) − (mass of products); a positive value means energy is released. Always convert mass to the same units first (kg with c² in joules, or u with the 931 MeV shortcut). |
Mass defect and binding energy: topic worksheet
6 questions, 48 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
A helium-4 nucleus is made of 2 protons and 2 neutrons. Use: proton mass = 1.00728 u, neutron mass = 1.00867 u, helium-4 nucleus mass = 4.00151 u.
(a) State what is meant by the mass defect of a nucleus. [1]
(b) Calculate the mass defect of the helium-4 nucleus, in u. [2]
(c) Calculate the binding energy, in MeV. [2]
(d) Calculate the binding energy per nucleon, in MeV. [2]
(e) State what the binding energy per nucleon tells you about the nucleus. [2]
Show how the conversion 1 u ≡ 931 MeV comes from E = mc².
(a) Calculate the energy equivalent of a mass of 1 u, in joules. [2]
(b) Convert this energy to MeV, and compare with 931 MeV. [2]
(c) State why mass and energy are treated as equivalent in nuclear physics. [2]
The binding energy per nucleon rises steeply for light nuclei, peaks near iron (A ≈ 56), then falls slowly toward the heaviest nuclei.
(a) State which nuclei are the most stable, and why. [2]
(b) Explain, using the curve, why energy is released when a heavy nucleus undergoes fission. [3]
(c) Explain why energy is released when two light nuclei undergo fusion. [2]
(d) State one reason fusion is hard to achieve on Earth. [1]
A deuterium and a tritium nucleus fuse: ²₁H + ³₁H → ⁴₂He + ¹₀n. Masses (u): ²₁H = 2.01410, ³₁H = 3.01605, ⁴₂He = 4.00260, n = 1.00867.
(a) Calculate the change in mass for the reaction, in u. [2]
(b) Calculate the energy released, in MeV. [2]
(c) Calculate the energy released, in joules. [2]
(d) State what happens to this energy. [2]
The Sun radiates energy at a power of 3.8 × 10²⁶ W, all of it coming from a loss of mass.
(a) State the relation between the power radiated and the rate of mass loss. [1]
(b) Calculate the mass lost by the Sun each second. [3]
(c) Suggest why this enormous rate barely changes the Sun's mass over a human lifetime. [2]
Radium-226 decays by alpha emission to radon: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. Masses (u): Ra-226 = 226.0254, Rn-222 = 222.0176, He-4 = 4.0026. The half-life of radium-226 is 1600 years.
(a) Show that the nucleon and proton numbers balance in the equation. [2]
(b) Calculate the change in mass, in u. [2]
(c) Calculate the energy released, in MeV and in joules. [3]
(d) Calculate the decay constant of radium-226, in s⁻¹ (1 year = 3.15 × 10⁷ s). [2]
(e) State whether the energy released per decay changes as the sample ages, and why. [2]
Answer key and marking notes
- (a)The difference between the total mass of the separate nucleons and the (smaller) mass of the nucleus ✓
- (b)Δm = 2(1.00728) + 2(1.00867) − 4.00151 ✓ = 4.03190 − 4.00151 = 0.03039 u ✓
- (c)BE = 0.03039 × 931 ✓ = 28.3 MeV ✓
- (d)28.3 / 4 ✓ = 7.07 MeV per nucleon ✓
- (e)It measures how tightly bound, and so how stable, the nucleus is ✓; a higher value means more energy is needed per nucleon to pull it apart ✓
- (a)E = mc² = 1.66 × 10⁻²⁷ × (3.00 × 10⁸)² ✓ = 1.49 × 10⁻¹⁰ J ✓
- (b)E = 1.49 × 10⁻¹⁰ / 1.60 × 10⁻¹³ ✓ = 933 MeV ≈ 931 MeV ✓
- (c)By E = mc² a change in mass corresponds to a change in energy ✓; in nuclear reactions the "missing" mass appears as released energy ✓
- (a)Nuclei near the peak (around iron) ✓; they have the greatest binding energy per nucleon, so are the most tightly bound ✓
- (b)A heavy nucleus lies to the right of the peak ✓; its fragments lie nearer the peak with a greater binding energy per nucleon ✓; the increase in binding energy is released as energy ✓
- (c)Light nuclei lie to the left; fusing them gives a nucleus nearer the peak with higher binding energy per nucleon ✓, so energy is released ✓
- (d)The nuclei must overcome strong electrostatic repulsion, needing very high temperatures and pressures ✓
- (a)Δm = (2.01410 + 3.01605) − (4.00260 + 1.00867) ✓ = 5.03015 − 5.01127 = 0.01888 u ✓
- (b)E = 0.01888 × 931 ✓ = 17.6 MeV ✓
- (c)E = 17.6 × 10⁶ × 1.60 × 10⁻¹⁹ ✓ = 2.81 × 10⁻¹² J ✓
- (d)It appears as kinetic energy of the products (the helium nucleus and the neutron) ✓✓
- (a)P = (Δm/Δt) c², so the rate of mass loss = P / c² ✓
- (b)Δm/Δt = 3.8 × 10²⁶ / (3.00 × 10⁸)² ✓ = 3.8 × 10²⁶ / 9.0 × 10¹⁶ ✓ = 4.2 × 10⁹ kg s⁻¹ ✓
- (c)The Sun's mass (about 2 × 10³⁰ kg) is vastly larger ✓; even over decades the fraction lost is negligible ✓
- (a)Nucleon: 226 = 222 + 4 ✓; proton: 88 = 86 + 2 ✓
- (b)Δm = 226.0254 − (222.0176 + 4.0026) ✓ = 226.0254 − 226.0202 = 0.0052 u ✓
- (c)E = 0.0052 × 931 ✓ = 4.8 MeV ✓ = 4.8 × 10⁶ × 1.60 × 10⁻¹⁹ = 7.7 × 10⁻¹³ J ✓
- (d)t½ = 1600 × 3.15 × 10⁷ = 5.04 × 10¹⁰ s; λ = 0.693 / 5.04 × 10¹⁰ ✓ = 1.4 × 10⁻¹¹ s⁻¹ ✓
- (e)No ✓; each decay involves the same nuclei and the same mass change, so the energy per decay is fixed; only the number of decays per second falls ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
Compared with the total mass of its separated nucleons, the mass of a nucleus is:
- Asmaller, by the mass defect
- Blarger, by the mass defect
- Cexactly the same
- Dzero
The binding energy of a nucleus is equal to:
- Athe mass defect multiplied by c²
- Bthe mass of the nucleus multiplied by c²
- Cthe mass defect divided by c²
- Dthe nucleon number multiplied by c
On the binding-energy-per-nucleon curve, the most stable nuclei are found:
- Anear the peak, around iron (A ≈ 56)
- Bat the lightest nuclei, around hydrogen
- Cat the heaviest nuclei, around uranium
- Dat nucleon number zero
Energy is released in both nuclear fusion and nuclear fission because the products have:
- Aa greater binding energy per nucleon
- Ba smaller binding energy per nucleon
- Ca larger total mass
- Dmore nucleons
Quiz key
Energy is released when the nucleus forms, so it has less mass than its separate parts. The difference is the mass defect Δm.
Binding energy = Δm c². It is the energy released as the nucleus forms, or the energy needed to separate it into individual nucleons.
The peak of the curve (about 8.8 MeV per nucleon, near iron) marks the most tightly bound, most stable nuclei.
Both processes move nucleons up toward the peak of the curve, increasing the binding energy per nucleon; the extra binding energy is released.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.