# Nuclear fission and fusion

> Physics · CIE A-Level 9702
> Source: https://www.owlsprep.com/study/cie-9702-u27-nuclear-fission-and-fusion/

This module explains the processes of nuclear fission and fusion, how mass defect produces energy, and the conditions required for sustained reactions, aligned to CIE A-Level 9702 exam expectations.

**Prerequisites:** [Mass defect and binding energy](https://www.owlsprep.com/study/cie-9702-u27-mass-defect-binding-energy/)

## Learning objectives

- Distinguish between the processes of nuclear fission and nuclear fusion
- Calculate mass defect and energy released in fission and fusion reactions
- Explain the conditions required for sustained fission and fusion
- Describe the role of chain reactions in nuclear fission

## Nuclear Fission: Definition and Energy Calculation

**Nuclear Fission** — A nuclear reaction in which a heavy unstable nucleus (typically uranium-235 or plutonium-239) splits into two smaller lighter nuclei, releasing a large amount of energy and free neutrons.

*Example:* $^{235}_{92}U + ^1_0n \rightarrow ^{92}_{36}Kr + ^{141}_{56}Ba + 3^1_0n$

Fission of heavy nuclei releases energy because heavy elements (mass number > 200) have lower binding energy per nucleon than elements with mass number around 100. The total binding energy of the products is higher than the reactants, so the mass defect is converted to kinetic energy, which is extracted as heat for power generation.

**Worked example:** Calculate the energy released in MeV for the fission reaction below, given: $m(^{235}U) = 235.0439$ u, $m(n) = 1.0087$ u, $m(^{92}Kr) = 91.9263$ u, $m(^{141}Ba) = 140.9144$ u. (1 u = 931.5 MeV/c²)

1. Calculate total mass of reactants:

   $$m_{\text{reactants}} = m(^{235}U) + m(n) = 235.0439 + 1.0087 = 236.0526 \text{ u}$$
2. Calculate total mass of products:

   $$m_{\text{products}} = m(^{92}Kr) + m(^{141}Ba) + 3m(n) = 91.9263 + 140.9144 + 3(1.0087) = 235.8668 \text{ u}$$
3. Calculate the mass defect:

   $$\Delta m = m_{\text{reactants}} - m_{\text{products}} = 236.0526 - 235.8668 = 0.1858 \text{ u}$$
4. Convert mass defect to energy using $E = \Delta m c^2$:

   $$E = 0.1858 \times 931.5 \approx 173 \text{ MeV}$$

> **tip**
>
> Always count all neutrons on both sides of the reaction equation when summing masses — missing the product neutrons is a very common exam mistake.

## Chain Reactions and Critical Mass

Each fission reaction releases 2-3 free neutrons. These neutrons can go on to induce fission in other nearby heavy nuclei, leading to a self-sustaining sequence of reactions called a chain reaction.

**Critical Mass** — The minimum mass of fissile material required to sustain a steady, controlled chain reaction. A sub-critical mass has too many neutron escapes, so the reaction stops. A super-critical mass leads to an exponential, runaway increase in reaction rate.

**Worked example:** Explain why a chain reaction cannot be sustained in a small sample of pure U-235.

1. A small sample of U-235 has a large surface area to volume ratio.
2. Most neutrons produced by fission pass through the small sample and escape into the surroundings, rather than colliding with another U-235 nucleus.
3. The number of new fission events triggered per reaction is less than 1, so the reaction dies out and cannot sustain.

## Nuclear Fusion: Definition and Requirements

**Nuclear Fusion** — A nuclear reaction in which two light nuclei combine to form a single heavier nucleus, releasing a large amount of energy.

*Example:* $^2_1H + ^3_1H \rightarrow ^4_2He + ^1_0n$

Fusion releases energy because light nuclei (mass number < 50) have lower binding energy per nucleon than iron (the most stable nucleus, with highest binding energy per nucleon). The total mass of the product is less than the total mass of the reactants, so the mass defect is converted to energy.

For fusion to occur, two positively charged nuclei must overcome the electrostatic Coulomb repulsion between them to get close enough for the strong nuclear force to bind them. This requires two key conditions:

1. Extremely high temperature ($> 10^7$ °C): gives nuclei enough kinetic energy to overcome repulsion
2. High pressure/density: keeps nuclei close together to increase the rate of collisions

**Worked example:** Compare the energy released per kg of fuel for fission of U-235 (200 MeV per fission) and D-T fusion (17.6 MeV per reaction). Why is fusion considered a better energy source?

1. Calculate energy per kg for fission: 1 kg U-235 has $\frac{1000}{235} \times N_A \approx 2.56 \times 10^{24}$ atoms

   $$E_{\text{fission}} = 2.56 \times 10^{24} \times 200 = 5.12 \times 10^{26} \text{ MeV/kg}$$
2. Calculate energy per kg for fusion: one D-T reaction has total mass 5 u, so 1 kg has $\frac{1000}{5} \times N_A \approx 1.2 \times 10^{26}$ reactions

   $$E_{\text{fusion}} = 1.2 \times 10^{26} \times 17.6 = 2.11 \times 10^{27} \text{ MeV/kg}$$
3. Conclusion: Fusion releases ~4 times more energy per kg of fuel than fission, and produces far less long-lived radioactive waste, making it a much cleaner energy source.

## Fission and Fusion in Context

Controlled nuclear fission is used commercially to generate electricity. Control rods made of neutron-absorbing material (e.g. boron) are used to adjust the reaction rate, keeping it critical (steady) rather than super-critical (runaway). Uncontrolled fission is the basis of atomic fission weapons.

Fusion is the natural process that powers all stars, including the Sun: the core of the Sun has enough temperature and pressure to sustain hydrogen fusion into helium, releasing the energy that radiates out to Earth. Fusion is not yet used for commercial power generation, though large-scale research projects like ITER are developing this technology.

## Common pitfalls

- **Wrong:** Forgetting to add the mass of the incident neutron when calculating mass defect for fission
  - Why it fails: Most fission reactions are induced by a neutron, so the neutron must be included on the reactant side
  - Correct: Always write out the full reaction equation and sum masses of *all* particles on both sides
- **Wrong:** Stating that energy is released because total binding energy of products is greater than reactants
  - Why it fails: CIE examiners require reference to binding energy *per nucleon*, not total binding energy, to get full marks
  - Correct: State that products have a higher binding energy per nucleon than reactants, so the excess energy is released
- **Wrong:** Claiming fusion releases more energy per reaction than fission
  - Why it fails: A single fission reaction releases ~200 MeV, while a single fusion reaction releases ~17 MeV
  - Correct: Correctly state that fusion releases more energy per *kilogram of fuel* than fission
- **Wrong:** Defining critical mass as the mass needed to start a chain reaction
  - Why it fails: Critical mass describes the condition to sustain a steady chain reaction, not start it
  - Correct: Define critical mass as the minimum mass of fissile material required to maintain a steady, self-sustaining chain reaction
- **Wrong:** Saying high pressure is needed for fusion to give nuclei more kinetic energy
  - Why it fails: High temperature gives nuclei kinetic energy; high pressure increases collision frequency by keeping nuclei close together
  - Correct: State high temperature overcomes Coulomb repulsion, high density/pressure increases reaction rate

## Cheatsheet

| Property | Nuclear Fission | Nuclear Fusion |
| --- | --- | --- |
| Core process | Heavy nucleus splits into two lighter nuclei | Two light nuclei combine into one heavier nucleus |
| Energy per reaction | ~200 MeV | ~17.6 MeV |
| Energy per kg fuel | ~$5 \times 10^{26}$ MeV/kg | ~$2 \times 10^{27}$ MeV/kg (4× higher) |
| Key conditions | Critical mass, slow neutrons for induced fission | $T > 10^7$ °C, high density to overcome Coulomb repulsion |

## What's next

Nuclear fission and fusion is a core topic that is regularly tested in both Paper 2 and Paper 4 of CIE A-Level Physics, often linked to calculations of energy release and comparisons of energy resources. Mastery of this topic relies on a solid understanding of binding energy and mass defect, so it is important to practice calculation questions to avoid common errors. You can now move on to related topics in nuclear physics and energy applications to build on this knowledge.

- [Radiation safety](https://www.owlsprep.com/study/cie-9702-u27-radiation-safety/)
- [Medical imaging](https://www.owlsprep.com/study/cie-9702-u28-overview/)
- [X-ray imaging](https://www.owlsprep.com/study/cie-9702-u28-x-ray-imaging/)

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