Nuclear fission and fusion

IB Physics SL· 30 min read

1. Energy Release from Fission and Fusion★★☆☆☆⏱ 10 min

📘 Definition

Nuclear Fission

A nuclear reaction where a heavy, unstable nucleus splits into two smaller, lighter nuclei of roughly equal mass, releasing large amounts of energy.

Example:

Fission of uranium-235 after absorption of a slow neutron.

📘 Definition

Nuclear Fusion

A nuclear reaction where two small, light nuclei combine to form a single heavier nucleus, releasing large amounts of energy.

Example:

Fusion of hydrogen nuclei into helium in the core of the Sun.

📐 Worked Example

Binding energy per nucleon of U-235 is 7.6 MeV. Binding energy per nucleon of fission products (two medium nuclei) is 8.5 MeV. Calculate the total energy released per fission of U-235.

1
Total number of nucleons in U-235 is 235, which is conserved in the reaction. Calculate initial total binding energy:
2
$BE_{\text{initial}} = 235 \times 7.6 = 1786 \text{ MeV}$
3
Calculate final total binding energy of the fission products:
4
$BE_{\text{final}} = 235 \times 8.5 = 1997.5 \text{ MeV}$
5
Energy released equals the increase in total binding energy, since higher binding energy corresponds to lower total mass:
6
$\Delta E = BE_{\text{final}} - BE_{\text{initial}} = 1997.5 - 1786 = 211.5 \text{ MeV}$

2. Nuclear Fission and Chain Reactions★★☆☆☆⏱ 12 min

When a heavy nucleus undergoes fission, an average of 2-3 neutrons are released per reaction. These neutrons can go on to trigger fission in other nearby nuclei, creating a self-sustaining chain reaction.

📘 Definition

Critical Mass

The minimum mass of fissile material required to sustain a steady chain reaction. If mass is below critical, too many neutrons escape the material without triggering new fission, and the reaction dies out.

📐 Worked Example

A U-235 fission reaction releases 2.5 neutrons per fission on average. 1.2 neutrons are absorbed by non-fissile material or escape the reactor core per reaction. Will the chain reaction be sustained?

1
Calculate the number of neutrons available to trigger new fission events per reaction:
2
$n_{\text{effective}} = 2.5 - 1.2 = 1.3$
3
For a sustained chain reaction, the effective number of neutrons per reaction must be at least 1:
4
Since $1.3 > 1$ , the chain reaction is supercritical and will be sustained.

3. Nuclear Fusion★★★☆☆⏱ 15 min

Fusion is the process that powers all stars, including the Sun. For fusion to occur, two positively charged light nuclei must be brought close enough together for the strong nuclear force to bind them. This requires overcoming the electrostatic (Coulomb) repulsion between the protons.

📘 Definition

Thermonuclear Fusion

Fusion reactions that require extremely high temperatures (over 100 million °C) to give nuclei enough kinetic energy to overcome Coulomb repulsion, plus extremely high pressure to push nuclei close enough together.

📐 Worked Example

Calculate the energy released in the fusion reaction: $_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He +_{0}^{1} n$ . Given masses: deuterium = 2.0141 u, tritium = 3.0161 u, helium = 4.0026 u, neutron = 1.0087 u. 1 u = 931.5 MeV/ $c^{2}$ .

1
Calculate total initial mass of reactants:
2
$m_{\text{initial}} = 2.0141 + 3.0161 = 5.0302 \text{ u}$
3
Calculate total final mass of products:
4
$m_{\text{final}} = 4.0026 + 1.0087 = 5.0113 \text{ u}$
5
Calculate mass defect (mass lost, converted to energy):
6
$\Delta m = m_{\text{initial}} - m_{\text{final}} = 0.0189 \text{ u}$
7
Convert mass defect to energy released using $E = Δ m c^{2}$ :
8
$\Delta E = 0.0189 \times 931.5 \approx 17.6 \text{ MeV}$

4. Fission vs Fusion Comparison★★★☆☆⏱ 10 min

Methods compared

Fission and fusion have very different practical properties and applications, compared below:

Nuclear Fission

Splitting heavy nuclei into lighter fragments

+ Pros: Commercially mature for large-scale power generation; High energy density, no operational greenhouse gas emissions

− Cons: Produces long-lived radioactive waste; Limited uranium resources, risk of accidents

Nuclear Fusion

Combining light nuclei into heavier nuclei

+ Pros: Near-limitless fuel from water; No long-lived radioactive waste, no meltdown risk

− Cons: Not yet commercially viable; Extreme technical requirements for temperature and containment

✓ Quick check

Test your understanding:

Which statement correctly describes fission and fusion?
- Both fission of heavy nuclei and fusion of light nuclei release energy
- Only fission releases energy
- Both processes involve splitting large nuclei
- Fission produces less radioactive waste than fusion
Reveal answer
Both fission of heavy nuclei and fusion of light nuclei release energy —
Correct. Both processes produce products with higher binding energy per nucleon than reactants, so both release energy.

5. Common Pitfalls

Wrong move:

Calculating energy released as initial binding energy minus final binding energy

Why:

Binding energy is the energy that holds the nucleus together; higher binding energy means lower total mass. Energy released is the increase in total binding energy.

Correct move:

Energy released: $Δ E = B E_{final} - B E_{initial} = Δ m c^{2}$ , where $Δ m = m_{initial} - m_{final}$

Wrong move:

Thinking critical mass is the maximum mass allowed for a safe chain reaction

Why:

Critical mass is the minimum mass required to sustain a chain reaction, not the maximum.

Correct move:

Remember: critical mass = minimum mass of fissile material for a sustained chain reaction

Wrong move:

Thinking only high pressure is required for fusion, no high temperature

Why:

Pressure brings nuclei close together, but temperature provides the kinetic energy to overcome electrostatic repulsion between protons.

Correct move:

Both extremely high temperature and high pressure are required for sustained fusion.

Wrong move:

Assuming all nuclear reactions release energy

Why:

Energy is only released if products have higher average binding energy per nucleon than reactants. Splitting light nuclei or fusing heavy nuclei absorbs energy.

Correct move:

Always reference the binding energy per nucleon curve to check if energy is released or absorbed.

6. Quick Reference Cheatsheet

Property	Nuclear Fission	Nuclear Fusion
Process	Heavy nucleus splits into lighter nuclei	Light nuclei combine into heavier nucleus
Energy per reaction	~200 MeV	~17 MeV
Energy per kg fuel	~10¹⁰ kWh/kg	~10¹¹ kWh/kg (10× fission)
Key requirements	Critical mass of fissile material, neutrons	T > 10⁸ °C, high pressure, confinement
Commercial power	Mature, widely used	Still in development
Radioactive waste	Large amounts of long-lived waste	Small amounts of short-lived waste

7. Frequently Asked

Why do both fission and fusion release energy?

Energy is released when reaction products have a higher average binding energy per nucleon than reactants. Fission of heavy nuclei and fusion of light nuclei both produce products closer to the peak of the binding energy per nucleon curve (the most stable region around iron/nickel), so both release energy.

When this came up on past exams

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

2023 · Paper 1
Energy release comparison of fusion/fission
2022 · Paper 2
Critical mass and fission chain reactions
2021 · Paper 1
Conditions required for nuclear fusion

Going deeper

syllabusOfficial IB Physics SL GuideFull syllabus reference for Unit 5

What's Next

Understanding fission and fusion completes your study of nuclear physics for IB Physics SL. These concepts explain energy production in stars, nuclear power generation, and are a common comparison topic for Paper 2 extended response questions. You will see these ideas referenced again in environmental physics topics when studying low-carbon energy production, and they form the foundation for higher-level nuclear physics study. Next, you will move on to the quantum physics section of Unit 5, starting with the photoelectric effect, one of the most important experiments for developing quantum theory.