Study Guide

Nuclear fission and fusion

PhysicsΒ· Unit 27: Nuclear PhysicsΒ· 15 min read

1. Nuclear Fission: Definition and Energy Calculationβ˜…β˜…β˜†β˜†β˜†β± 5 min

πŸ“˜ Definition

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:

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.

πŸ“ Worked Example

Calculate the energy released in MeV for the fission reaction below, given: u, u, u, u. (1 u = 931.5 MeV/cΒ²)

  1. 1

    Calculate total mass of reactants:

    mreactants=m(235U)+m(n)=235.0439+1.0087=236.0526 um_{\text{reactants}} = m(^{235}U) + m(n) = 235.0439 + 1.0087 = 236.0526 \text{ u}
  2. 2

    Calculate total mass of products:

    mproducts=m(92Kr)+m(141Ba)+3m(n)=91.9263+140.9144+3(1.0087)=235.8668 um_{\text{products}} = m(^{92}Kr) + m(^{141}Ba) + 3m(n) = 91.9263 + 140.9144 + 3(1.0087) = 235.8668 \text{ u}
  3. 3

    Calculate the mass defect:

    Ξ”m=mreactantsβˆ’mproducts=236.0526βˆ’235.8668=0.1858 u\Delta m = m_{\text{reactants}} - m_{\text{products}} = 236.0526 - 235.8668 = 0.1858 \text{ u}
  4. 4

    Convert mass defect to energy using :

    E=0.1858Γ—931.5β‰ˆ173 MeVE = 0.1858 \times 931.5 \approx 173 \text{ MeV}

2. Chain Reactions and Critical Massβ˜…β˜…β˜†β˜†β˜†β± 4 min

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.

πŸ“˜ Definition

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.

πŸ“ Worked Example

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

  1. 1

    A small sample of U-235 has a large surface area to volume ratio.

  2. 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. 3

    The number of new fission events triggered per reaction is less than 1, so the reaction dies out and cannot sustain.

3. Nuclear Fusion: Definition and Requirementsβ˜…β˜…β˜…β˜†β˜†β± 5 min

πŸ“˜ Definition

Nuclear Fusion

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

Example:

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 ( Β°C): gives nuclei enough kinetic energy to overcome repulsion

  2. High pressure/density: keeps nuclei close together to increase the rate of collisions

πŸ“ 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. 1

    Calculate energy per kg for fission: 1 kg U-235 has atoms

    Efission=2.56Γ—1024Γ—200=5.12Γ—1026 MeV/kgE_{\text{fission}} = 2.56 \times 10^{24} \times 200 = 5.12 \times 10^{26} \text{ MeV/kg}
  2. 2

    Calculate energy per kg for fusion: one D-T reaction has total mass 5 u, so 1 kg has reactions

    Efusion=1.2Γ—1026Γ—17.6=2.11Γ—1027 MeV/kgE_{\text{fusion}} = 1.2 \times 10^{26} \times 17.6 = 2.11 \times 10^{27} \text{ MeV/kg}
  3. 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.

4. Fission and Fusion in Contextβ˜…β˜…β˜†β˜†β˜†β± 3 min

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.

5. Common Pitfalls

Wrong move:

Forgetting to add the mass of the incident neutron when calculating mass defect for fission

Why:

Most fission reactions are induced by a neutron, so the neutron must be included on the reactant side

Correct move:

Always write out the full reaction equation and sum masses of all particles on both sides

Wrong move:

Stating that energy is released because total binding energy of products is greater than reactants

Why:

CIE examiners require reference to binding energy per nucleon, not total binding energy, to get full marks

Correct move:

State that products have a higher binding energy per nucleon than reactants, so the excess energy is released

Wrong move:

Claiming fusion releases more energy per reaction than fission

Why:

A single fission reaction releases ~200 MeV, while a single fusion reaction releases ~17 MeV

Correct move:

Correctly state that fusion releases more energy per kilogram of fuel than fission

Wrong move:

Defining critical mass as the mass needed to start a chain reaction

Why:

Critical mass describes the condition to sustain a steady chain reaction, not start it

Correct move:

Define critical mass as the minimum mass of fissile material required to maintain a steady, self-sustaining chain reaction

Wrong move:

Saying high pressure is needed for fusion to give nuclei more kinetic energy

Why:

High temperature gives nuclei kinetic energy; high pressure increases collision frequency by keeping nuclei close together

Correct move:

State high temperature overcomes Coulomb repulsion, high density/pressure increases reaction rate

6. Quick Reference 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

~ MeV/kg

~ MeV/kg (4Γ— higher)

Key conditions

Critical mass, slow neutrons for induced fission

Β°C, high density to overcome Coulomb repulsion

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7. Frequently Asked

What is the key distinction between fission and fusion expected in CIE exams?

Fission splits a heavy nucleus into smaller lighter nuclei, while fusion combines light nuclei into a heavier nucleus. Always state this clearly for 2-mark distinction questions.

Why do both fission and fusion release energy?

Both processes produce products with a higher binding energy per nucleon than the reactants. The mass defect from this difference is converted to energy via .

When this came up on past exams

AI-estimated based on syllabus patterns β€” cross-check with official past papers for accuracy. Use only as revision-focus signals.

  • 2022 Β· 2

    Energy calculation for fission

  • 2021 Β· 4

    Compare fission/fusion conditions

  • 2023 Β· 2

    Explanation of critical mass

  • 2020 Β· 4

    Conditions for nuclear fusion

Going deeper

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.