E.6 Fission and fusion (AHL)

IB Physics HL· 45 min read

1. Energy Release from Fission and Fusion★★☆☆☆⏱ 15 min

Both processes release energy because of the shape of the binding energy per nucleon (BE/A) curve. Intermediate mass nuclei (A ≈ 56) have the highest BE/A, so splitting heavy nuclei (fission) or joining light nuclei (fusion) produces more tightly bound products, with excess energy released.

📘 Definition

Mass-Energy Equivalence

The energy released in a nuclear reaction is equal to the mass defect multiplied by the speed of light squared.

Example:

A mass defect of 1 u corresponds to 931.5 MeV of released energy

E = \Delta m c^2 \quad \text{where} \quad \Delta m = m_{\text{reactants}} - m_{\text{products}}

📐 Worked Example

Calculate the energy released in the fission reaction: $_{92}^{235} U +_{0}^{1} n \to_{56}^{141} Ba +_{36}^{92} Kr + 3_{0}^{1} n$ . Given masses: $m (U - 235) = 235.0439$ u, $m (n) = 1.0087$ u, $m (B a - 141) = 140.9144$ u, $m (K r - 92) = 91.9262$ u. 1 u = 931.5 MeV/c².

1
Calculate total mass of reactants:
$m_{\text{reactants}} = 235.0439 + 1.0087 = 236.0526 \text{ u}$
2
Calculate total mass of products:
$m_{\text{products}} = 140.9144 + 91.9262 + (3 \times 1.0087) = 235.8667 \text{ u}$
3
Find the positive mass defect:
$\Delta m = 236.0526 - 235.8667 = 0.1859 \text{ u}$
4
Convert mass defect to energy released:
$E = 0.1859 \times 931.5 \approx 173 \text{ MeV}$

2. Nuclear Fission and Chain Reactions★★☆☆☆HL only⏱ 20 min

When a heavy fissile nucleus absorbs a neutron and undergoes fission, it releases multiple new neutrons. These neutrons can trigger fission in other nearby nuclei, creating a multiplying chain reaction.

📘 Definition

Critical Chain Reaction

A steady chain reaction where exactly one neutron from each fission event goes on to cause another fission, maintaining constant power output.

In commercial nuclear reactors, neutron-absorbing control rods (made of boron or cadmium) are adjusted to maintain a critical state. Subcritical reactions (k < 1) die out, while supercritical reactions (k > 1) grow exponentially.

📐 Worked Example

A reactor starts with 1 neutron in generation 1. The neutron multiplication factor $k = 1.01$ . How many neutrons are present in generation 100?

1
The number of neutrons after $n - 1$ generations follows the exponential growth rule:
$N_n = k^{n-1}$
2
Substitute $n = 100$ and $k = 1.01$ :
$N_{100} = (1.01)^{99} \approx 2.7$
3
Interpret the result: the number of neutrons slowly increases, so control rods must be adjusted to reduce $k$ to 1 for steady power.

3. Nuclear Fusion★★★☆☆HL only⏱ 20 min

Nuclear fusion joins two light positively charged nuclei to form a heavier nucleus. For fusion to occur, the nuclei must overcome electrostatic Coulomb repulsion between them, which requires extremely high temperatures (≥ 10⁷ K) and high density to produce frequent energetic collisions.

📘 Definition

Coulomb Repulsion

The electrostatic force that repels two positively charged atomic nuclei, which must be overcome for fusion to occur.

📐 Worked Example

Calculate the energy released in the deuterium-tritium fusion reaction: $_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He +_{0}^{1} n$ . Given masses: $m (^{2} H) = 2.0141$ u, $m (^{3} H) = 3.0160$ u, $m (^{4} He) = 4.0026$ u, $m (n) = 1.0087$ u.

1
Calculate total mass of reactants:
$m_{\text{reactants}} = 2.0141 + 3.0160 = 5.0301 \text{ u}$
2
Calculate total mass of products:
$m_{\text{products}} = 4.0026 + 1.0087 = 5.0113 \text{ u}$
3
Calculate energy released:
$E = (5.0301 - 5.0113) \times 931.5 \approx 17.5 \text{ MeV}$

4. Exam Command Term Guidance★★☆☆☆⏱ 10 min

5. Common Pitfalls

Wrong move:

Calculating mass defect as product mass minus reactant mass

Why:

This gives a negative Δm, which can lead to confusion and lost marks for exothermic reactions

Correct move:

Always calculate Δm = m_reactants - m_products to get a positive value for energy released

Wrong move:

Claiming fusion releases more energy per reaction than fission

Why:

Per individual reaction, fission releases ~170-200 MeV, while fusion releases ~10-20 MeV

Correct move:

State that fusion releases more energy per unit mass of fuel, not per reaction

Wrong move:

Confusing critical, subcritical and supercritical chain reaction states

Why:

Students often mix up the value of the multiplication factor k for each state

Correct move:

k<1 = subcritical (dies out), k=1 = critical (steady), k>1 = supercritical (grows)

Wrong move:

Thinking the Sun's core is hotter than fusion reactors on Earth

Why:

The Sun has extremely high core pressure, so fusion proceeds at lower temperatures than Earth-based reactors

Correct move:

Remember Earth fusion reactors need higher temperatures to compensate for lower pressure

6. Quick Reference Cheatsheet

Property	Nuclear Fission	Nuclear Fusion
Reactant nuclei	Heavy (A > 200)	Light (A < 20)
Energy per reaction	~170-200 MeV	~10-20 MeV
Energy per kg fuel	~8 × 10¹³ J	~3 × 10¹⁴ J (4× fission)
Required conditions	Critical mass of fissile material	T > 10⁷ K, plasma confinement
Waste	Long-lived highly radioactive waste	Low-level short-lived waste
Commercial use	Mature technology	Still in development

7. Frequently Asked

Why does fusion release more energy per kg than fission?

Fusion of light nuclei produces a larger increase in binding energy per nucleon per unit mass than fission of heavy nuclei, leading to ~3-4 times more energy released per kilogram of fuel.

Going deeper

syllabusOfficial IB Physics HL 2025 SyllabusFull syllabus reference for Theme E

What's Next

This topic builds on your understanding of binding energy and mass defect to explain two of the most important energy-releasing nuclear processes in physics. Mastery of fission and fusion is essential for understanding stellar evolution, nucleosynthesis, and nuclear energy production, which are common long-answer topics in IB Physics HL exams. The concepts here also connect directly to real-world energy debates and modern physics research into sustainable power. Below are related topics to explore next to deepen your understanding.