# Nuclear fission and fusion

> IB Physics SL · Unit 5: Nuclear and quantum physics
> Source: https://www.owlsprep.com/study/ib-physics-sl-u5-nuclear-fission-and-fusion/

This sub-topic explains the core processes of nuclear fission and fusion, how energy is released from both reactions via mass defect, and the physical conditions required for sustained energy-producing reactions, a common exam topic for IB Physics SL.

**Prerequisites:** [Binding energy and mass defect](https://www.owlsprep.com/study/ib-physics-sl-u5-binding-energy-and-mass-defect/)

## Learning objectives

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

## Energy Release from Fission and Fusion

**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.

**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.

> **info**
>
> Energy is released from any nuclear reaction where products have a higher average binding energy per nucleon than reactants. The binding energy per nucleon curve peaks near mass number 56 (iron), so fission of heavy nuclei and fusion of light nuclei both release energy.

**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. $$\Delta E = BE_{\text{final}} - BE_{\text{initial}} = 1997.5 - 1786 = 211.5 \text{ MeV}$$

## Nuclear Fission and Chain Reactions

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.

**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.

> **Exam tip**
>
> In nuclear reactors, control rods absorb excess neutrons to keep the effective number of neutrons equal to 1, maintaining a steady, controlled chain reaction.

## Nuclear Fusion

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.

**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: $^2_1\text{H} + ^3_1\text{H} \rightarrow ^4_2\text{He} + ^1_0\text{n}$. 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 $E = \Delta m c^2$:
8. $$\Delta E = 0.0189 \times 931.5 \approx 17.6 \text{ MeV}$$

> **info**
>
> Controlled thermonuclear fusion for commercial power generation is not yet technologically mature, but it offers the potential for near-limitless clean energy with minimal radioactive waste.

## Fission vs Fusion Comparison

**Comparing methods**

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

**Check your understanding**

Test your understanding:

1. 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

   *Why:* Correct. Both processes produce products with higher binding energy per nucleon than reactants, so both release energy.

## Common pitfalls

- **Wrong:** Calculating energy released as initial binding energy minus final binding energy
  - Why it fails: 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: Energy released: $\Delta E = BE_{\text{final}} - BE_{\text{initial}} = \Delta m c^2$, where $\Delta m = m_{\text{initial}} - m_{\text{final}}$
- **Wrong:** Thinking critical mass is the maximum mass allowed for a safe chain reaction
  - Why it fails: Critical mass is the minimum mass required to sustain a chain reaction, not the maximum.
  - Correct: Remember: critical mass = minimum mass of fissile material for a sustained chain reaction
- **Wrong:** Thinking only high pressure is required for fusion, no high temperature
  - Why it fails: Pressure brings nuclei close together, but temperature provides the kinetic energy to overcome electrostatic repulsion between protons.
  - Correct: Both extremely high temperature and high pressure are required for sustained fusion.
- **Wrong:** Assuming all nuclear reactions release energy
  - Why it fails: 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: Always reference the binding energy per nucleon curve to check if energy is released or absorbed.

## 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 |

## 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.

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