Binding energy in fusion and fission

Key idea: A reviewed, static H2 Physics learning chain for all official Nuclear Physics outcomes, from Rutherford evidence to fusion and fission.

  • GCE A-Level H2 Physics 2027

Learn the idea

Big question: Why can both joining light nuclei and splitting heavy nuclei release energy?

Fusion and fission can move products toward the maximum of the binding-energy-per-nucleon curve. The products then have greater total binding energy and lower total rest mass, so the difference is released as kinetic energy and radiation. The same binding-energy argument explains both processes; the curve must be used to compare complete reactant and product systems.

Compare total binding before and after

Both processes can move nuclei towards the higher binding-energy-per-nucleon region near iron. Fusion joins suitable light nuclei; fission splits a very heavy nucleus into medium-mass products.

Multiply binding energy per nucleon by nucleon number when comparing totals. If products have greater total binding energy, they have lower total rest mass, and the difference appears as kinetic energy and radiation. Total mass-energy remains conserved.

Check your understanding: Products gain 3.0 MeV of total binding energy. What energy is released?

3.0 MeV, corresponding to a rest-mass decrease of 3.0 MeV/c².

Do not overread the curve

The curve shows the general direction in which binding energy per nucleon increases; it does not say that every imaginable fusion or fission reaction will occur. A proposed process must still conserve nucleon number, charge, mass-energy and momentum.

To calculate an energy release, compare the total mass-energy or total binding energy of the complete reactant and product systems. Comparing only two vertical curve heights can be misleading when the systems contain different numbers of nucleons.

Check your understanding: Why is a higher product binding energy per nucleon not by itself a complete energy calculation?

Energy release depends on the change in total binding energy for all nucleons in the complete reaction, not only on two average values.

Binding energy per nucleon curveBinding energy per nucleon rises steeply for light nuclei, reaches a broad maximum near iron and nickel, then decreases slowly for heavy nuclei. Arrows show fusion and fission moving toward the maximum.Nucleon number, ABinding energy per nucleonFe / Ni regionlightheavyfusionfissionproducts more tightly bound on average
Scroll diagram horizontally to read all labels.
Fusion of light nuclei and fission of very heavy nuclei can move products toward greater binding energy per nucleon. The increase in total binding energy is released.

Key ideas to keep

  • Energy release depends on total binding energy, not only binding energy per nucleon.
  • Fusion releases energy for light nuclei; joining arbitrary heavy nuclei does not.
  • Conservation of mass-energy replaces separate mass conservation.

Worked example

Use one binding-energy curve for two processes

Question: Use the binding-energy-per-nucleon curve to compare deuterium fusion and uranium fission.

  1. Step 1: Locate the reactants

    Why: Light and very heavy nuclei lie on opposite sides of the curve's maximum.

    Working: Light nuclei lie on the steep rising side; uranium lies on the slowly falling heavy side.

  2. Step 2: Locate the products

    Why: Both processes can move nuclei towards the iron-region maximum.

    Working: Fusion products and medium-mass fission products have greater binding energy per nucleon.

  3. Step 3: State the conserved energy account

    Why: Greater total binding means lower product rest mass.

    Working: The rest-mass decrease is released as kinetic energy and radiation while total mass-energy remains conserved.

Answer: Light nuclei rise steeply toward the iron-region maximum when fused; very heavy nuclei move upward when split into medium nuclei. The increase in total binding energy is released.

Check: Compare total binding energy, not only the height of one point on the per-nucleon graph.

Practise with support

Try this

Products have higher binding energy per nucleon. State the energy sign.

Hint: More tightly bound means lower system energy.

Check your answer

Energy is released; the products have lower total mass-energy.

Practise independently

Your turn

Explain fusion and fission using the curve rather than saying that mass disappears.

Check your answer

Both can move products toward the curve's higher binding-energy-per-nucleon region. Greater total binding lowers product mass-energy, and the difference appears as kinetic energy and radiation.

Common mistakes

Common mistake

Fusion and fission release energy for opposite unrelated reasons.

What is wrong with this reasoning?

Show better thinking

Both can move products toward higher binding energy per nucleon.

Exam guidance

Use the curve to compare initial and final total binding energies, then state where the released energy appears.

Exam-style practice [5 marks]

A reaction increases total binding energy by 3.2 MeV. State mass change and energy output.

Plan before you answer

  • Compare total binding energies.
  • Translate the increase to a mass change.
  • State where the energy appears.
Mark your answer and compare the model

Marking points

Tick each point only if your answer states it clearly.

Model answer

Mass decreases by Δm = 3.2 MeV/c² and 3.2 MeV is released.

Check what stayed with you

Recall question

What single curve feature permits energy release in both processes?

Check the answer

Both product sets can lie higher on the binding-energy-per-nucleon curve than their reactants.

Try this next

Use the longer mixed questions to connect the ideas, calculations and diagrams from this topic.

Open Nuclear Physics structured practice

Syllabus and review details

This lesson covers the listed H2 Physics 9478 outcomes. Topic 20 excludes knowledge of positron emission in 20(g) and detailed knowledge of the antineutrino and particle zoo in 20(o). Nuclide equations conserve nucleon number, charge, mass-energy and momentum. Count data require background correction before population-law inference. Applications must relate half-life, penetration and ionisation to benefit and hazard. The binding-energy-per-nucleon curve, not a claim that mass disappears, explains fusion and fission energy release.

  • GCE A-Level H2 PhysicsTopic 20(t) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027