Fission, fusion & mass–energy equivalence

Learning goals

What students should be able to explain, calculate and investigate after completing Fission, Fusion and Mass-Energy Equivalence.

Goals marked Higher Level are required only for Higher Level students; the remaining goals are for all students.

• Describe nuclear fission and nuclear fusion, and explain why both release energy.
• Use the binding-energy-per-nucleon curve to explain why fission and fusion release energy.
• Higher Level: Describe controlled and uncontrolled chain reactions.
• Evaluate issues around nuclear fission and fusion for electricity generation.
• Higher Level: Describe positron-electron annihilation as a matter-antimatter interaction.

Key definitions

Precise terms, symbols and SI units used in Fission, Fusion and Mass-Energy Equivalence.

Why Fission and Fusion Both Release Energy

Fission and fusion can release energy when their products have lower total mass-energy than their reactants.

On the binding-energy-per-nucleon curve, both splitting very heavy nuclei and joining very light nuclei can produce more tightly bound nuclei. Iron-56 lies near the top of this curve and is commonly used as a reference for very tightly bound nuclei, but it should not be described as the exact universal maximum. The products then have lower total mass-energy than the reactants; the mass difference corresponds through E = Δmc² to the energy released. Binding energy per nucleon is useful evidence, but it is not the only factor affecting whether a particular nucleus is stable.

Nuclear Fission

In nuclear fission, a neutron is absorbed by a heavy fissile nucleus, which splits into two lighter nuclei and releases energy and additional neutrons.

A slow neutron absorbed by uranium-235 forms an unstable uranium-236 nucleus. It deforms and splits into two medium-mass nuclei, typically releasing two or three neutrons and energy mainly as kinetic energy of the fragments. If enough released neutrons cause further fissions, a chain reaction develops. In a power reactor it is held critical: on average one neutron from each fission causes one further fission.

Nuclear Fusion

In nuclear fusion, two light nuclei (e.g. isotopes of hydrogen) combine to form a heavier nucleus, releasing energy.

Because nuclei are positively charged, they strongly repel each other electrostatically, so fusion requires extremely high temperatures and pressures (as found in the core of the Sun) to force nuclei close enough for the (much stronger, but very short-range) nuclear force to bind them together. Fusion releases even more energy per unit mass of fuel than fission, and its fuel (isotopes of hydrogen) is abundant, but achieving controlled, sustained fusion for practical electricity generation on Earth remains a major ongoing engineering and scientific challenge.

Evaluating Fission and Fusion for Electricity Generation

Fission is an established source of continuous low-carbon electricity, while fusion is a potential future source that still faces major engineering and commercial challenges.

Evaluation means weighing evidence, benefits, limitations and present feasibility rather than merely describing a reactor. Fission power stations already generate electricity: controlled chain reactions heat a coolant, which ultimately produces steam for a turbine-generator. Their advantages include reliable large-scale output and very low operational greenhouse-gas emissions. Their limitations include high construction and decommissioning costs, accident and security risks that require multiple engineered safeguards, and radioactive waste that must be isolated and managed for long periods. Fusion could use abundant deuterium and produces no self-sustaining chain reaction, but deuterium–tritium systems still produce energetic neutrons, require tritium breeding and create activated reactor materials. Sustaining and controlling a plasma hot enough for useful net electrical output remains an engineering challenge; fusion is not currently a commercial source of grid electricity.

• Fuel contains fissile nuclei.
• A moderator slows neutrons; control rods absorb them.
• Coolant removes thermal energy; shielding reduces exposure.

How to evaluate: state the evidence, compare benefits with limitations, distinguish present capability from future potential, and finish with a justified conclusion.

Official curriculum basis: NCCA Leaving Certificate Physics specification, learning outcome 4.6.2. Scientific status references: IAEA Fusion FAQ and IAEA demonstration fusion plants.

Positron-Electron Annihilation

When an electron and a positron meet, their mass and kinetic energy are converted into electromagnetic radiation, normally two gamma-ray photons.

The rest energy of one electron is 0.511 MeV. An electron and positron annihilating at rest therefore produce a total photon energy of 1.022 MeV. One photon alone could not conserve both energy and momentum for a pair initially at rest; two oppositely directed photons can.

• A positron is the antiparticle of the electron. It has the same mass as an electron but charge +e.
• Electron–positron annihilation conserves energy, momentum and electric charge.
• If the pair is initially at rest, two gamma photons are produced in opposite directions so that total momentum remains zero.
• The value 1.022 MeV is the combined rest energy of an electron and positron initially at rest. Any initial kinetic energy also appears in the total photon energy.

Worked example: An electron and positron annihilate from rest. Each photon has energy 0.511 MeV. Using E = hf, the frequency of each photon is approximately 1.24 × 10²⁰ Hz.

Diagrams and formulae

Key diagrams and equations for reviewing Fission, Fusion and Mass-Energy Equivalence.

• Binding energy per nucleon vs mass number: the peak near iron-56 explains why both fission (heavy → medium) and fusion (light → medium) release energy, moving nuclei towards greater stability.
• Nuclear fission: a neutron striking a heavy nucleus causes it to split into two lighter fragments, releasing more neutrons and energy — the released neutrons can go on to sustain a chain reaction.
• Nuclear fusion: two light nuclei combine to form a heavier nucleus, releasing energy (e.g. deuterium + tritium → helium + neutron + energy).

Binding energy per nucleon vs mass number: the peak near iron-56 explains why both fission (heavy → medium) and fusion (light → medium) release energy, moving nuclei towards greater stability.

Nuclear fission: a neutron striking a heavy nucleus causes it to split into two lighter fragments, releasing more neutrons and energy — the released neutrons can go on to sustain a chain reaction.

Nuclear fusion: two light nuclei combine to form a heavier nucleus, releasing energy (e.g. deuterium + tritium → helium + neutron + energy).

• Key relationships
• Mass-energy equivalence: E = mc² Energy released = (mass defect between reactants and products) × c²

Worked Example

A step-by-step calculation applying the central relationships in Fission, Fusion and Mass-Energy Equivalence.

A fission reaction releases a mass defect of 3.2 × 10⁻²⁸ kg. Calculate the energy released. (c = 3 × 10⁸ m s⁻¹.)

• E = mc² = 3.2 × 10⁻²⁸ × (3 × 10⁸)²
• E = 3.2 × 10⁻²⁸ × 9 × 10¹⁶ = 2.88 × 10⁻¹¹ J

Practical / Investigation

Experimental planning, measurement and evaluation for Fission, Fusion and Mass-Energy Equivalence.

Investigation: Evaluating issues around nuclear fission and fusion using secondary sources

• Task: research and compare current nuclear fission power generation with the state of fusion research (e.g. tokamak or laser-based approaches), using reputable secondary sources.
• Evaluate criteria: carbon emissions, waste production and storage, fuel availability, safety record, and current technological readiness.
• Nature of Science link: this is a good example of weighing evidence and evaluating a real, currently unresolved scientific and engineering challenge, rather than a settled textbook fact.

• Define comparison criteria before collecting evidence: lifecycle emissions, waste, fuel, safety, output reliability and technological readiness.
• Use current primary or institutional sources, record publication dates, and separate measured performance from forecasts or proposed designs.
• A justified conclusion should acknowledge trade-offs and uncertainty; an independent/dependent-variable template is not appropriate here.

Quick-Check Questions

Short retrieval questions covering the essential ideas in Fission, Fusion and Mass-Energy Equivalence.

1. Define nuclear fission and nuclear fusion.

2. Why does fusion require extremely high temperature and pressure?

3. Distinguish a controlled from an uncontrolled chain reaction.

4. Explain, using the binding-energy-per-nucleon curve, why both fission and fusion can release energy.

5. What happens to the mass of an electron and a positron when they annihilate?

Common mistakes and exam tips

Common misconceptions and exam-technique checks for Fission, Fusion and Mass-Energy Equivalence.

• Avoid: Saying fission and fusion release energy for unrelated reasons. Correct idea: Both can form products with greater binding energy per nucleon, so mass-energy is released.
• Avoid: Describing a controlled chain reaction as one in which every emitted neutron causes fission. Correct idea: Control keeps the average number of further fissions per fission close to one.
• Avoid: Saying annihilation destroys mass and energy. Correct idea: The particle–antiparticle rest mass and other energy are converted into photon energy; total energy is conserved.

• Use the binding-energy-per-nucleon curve when explaining energy release.
• Distinguish a controlled chain reaction from an uncontrolled one using the average number of continuing fissions.
• Square c carefully before using E = mc².

Exam-style questions

Five exam-style questions with worked answers on Fission, Fusion and Mass-Energy Equivalence.

Higher Level — Required Content

Required Higher Level content for this topic.

• In a controlled chain reaction, control rods absorb neutrons so energy is released steadily.
• In an uncontrolled chain reaction, the number of fissions rises rapidly.

When an electron and positron annihilate, their mass and kinetic energy are converted into photon energy while energy and momentum are conserved.

End-of-unit revision

Formulae, definitions, experiments and mixed revision questions for Fission, Fusion and Mass-Energy Equivalence.

• E = mc² (energy released = mass defect × c²)

• Nuclear fission
• Nuclear fusion
• Controlled vs uncontrolled chain reaction
• Annihilation

• Binding energy per nucleon vs mass number, with fission and fusion directions marked
• Fission chain-reaction diagram
• Fusion reaction diagram

• Evaluating fission/fusion issues for electricity generation using secondary sources

• Thinking fission/fusion release energy for different underlying reasons
• Confusing controlled and uncontrolled chain reactions
• Thinking fusion is already used commercially for electricity

1. Explain the condition needed for a fission chain reaction to continue.

2. A reaction releases 9 × 10⁻¹³ J of energy. Calculate the mass defect responsible.

3. State two factors that should be weighed when evaluating nuclear fission as a method of electricity generation.

4. Explain what happens during positron-electron annihilation.

1. A chain reaction continues when, on average, at least one neutron from each fission causes another nucleus to undergo fission.

2. E = mc² → m = E/c² = (9×10⁻¹³) ÷ (9×10¹⁶) = 1×10⁻²⁹ kg.

3. Any two of: carbon emissions during operation, radioactive waste production/storage, fuel availability, safety record, cost of construction and decommissioning.

4. An electron and a positron (its antiparticle) meet and their combined rest mass is completely converted into energy, typically emitted as a pair of gamma-ray photons.

The table below shows which equations from this unit appear in the official State Examinations Commission Formulae and Tables book, and where.

The current specification includes fission and fusion for all students; controlled and uncontrolled chain reactions and positron–electron annihilation are identified as Higher Level content.