A-Level — physicsHard4 min read

Nuclear Energy, Fission, and Fusion

E = mc²; binding energy; mass defect; fission and fusion reactions

Tutor AI Team2026-02-25T05:30:41.205Z

# Nuclear Energy, Fission, and Fusion — A-Level Physics

Nuclear reactions release millions of times more energy than chemical reactions. Understanding mass-energy equivalence ( $E = mc^2$ ), binding energy, and the mechanisms of fission and fusion is essential at A-Level.

1. Mass-Energy Equivalence

$\boxed{E = mc^2}$

Mass and energy are interchangeable. When a nucleus is assembled from nucleons, some mass "disappears" — it becomes binding energy.

Atomic Mass Unit

$1\text{ u} = 1.661 \times 10^{-27}$ kg = 931.5 MeV/c²

2. Mass Defect and Binding Energy

Mass defect ( $\Delta m$ ): the difference between the total mass of individual nucleons and the actual mass of the nucleus.

$\Delta m = [Zm_p + (A-Z)m_n] - m_{\text{nucleus}}$

Binding energy ( $BE$ ): the energy equivalent of the mass defect — the energy needed to completely separate the nucleus into individual nucleons.

$BE = \Delta m \times c^2$

Binding energy per nucleon = $BE/A$ — measures the stability of a nucleus.

The Binding Energy Curve

Peak at iron-56 (~8.8 MeV per nucleon) — most stable nucleus
Light nuclei (left of Fe): can gain stability through fusion
Heavy nuclei (right of Fe): can gain stability through fission
Products always have higher BE per nucleon → energy is released

3. Nuclear Fission

A heavy nucleus splits into two lighter nuclei (+ neutrons + energy).

Example: $^{235}_{92}U + ^1_0 n \to ^{141}_{56}Ba + ^{92}_{36}Kr + 3^1_0 n + \text{energy}$

Chain Reaction

Each fission produces 2–3 neutrons
These can trigger further fissions
Critical mass needed for a sustained reaction

Nuclear Reactor

Fuel: enriched uranium (U-235) or plutonium
Moderator: slows neutrons (graphite or water) — thermal neutrons more likely to cause fission
Control rods: absorb neutrons (boron/cadmium) — regulate the reaction
Coolant: transfers heat to generate steam

4. Nuclear Fusion

Light nuclei combine to form a heavier nucleus.

$^2_1 H + ^3_1 H \to ^4_2 He + ^1_0 n + 17.6 \text{ MeV}$

Why Is Fusion Difficult?

Nuclei are positive → strong electrostatic repulsion
Need temperatures >100 million K (plasma)
Need to confine the plasma long enough (magnetic confinement — tokamak)

Advantages of Fusion

Virtually unlimited fuel (deuterium from seawater)
No long-lived radioactive waste
No carbon emissions
No risk of meltdown

Worked Example: Mass Defect

Problem

Helium-4: $Z = 2, A = 4$ . $m_p = 1.00728$ u, $m_n = 1.00867$ u, $m_{He} = 4.00260$ u.

$\Delta m = 2(1.00728) + 2(1.00867) - 4.00260$ $= 2.01456 + 2.01734 - 4.00260 = 0.02930$ u

$BE = 0.02930 \times 931.5 = 27.3$ MeV $BE/A = 27.3/4 = 6.82$ MeV/nucleon

Solution

Worked Example: Energy from Fission

Problem

U-235 fission releases ~200 MeV per event. How much energy from 1 kg?

Number of atoms = $1000/235 \times 6.02 \times 10^{23} = 2.56 \times 10^{24}$ Total energy = $2.56 \times 10^{24} \times 200 \times 10^6 \times 1.6 \times 10^{-19}$ $= 8.19 \times 10^{13}$ J ≈ 82 TJ

(Compare: 1 kg of coal releases ~30 MJ — nuclear is ~3 million times more energy-dense!)

Solution

6. Practice Questions

1. Explain the difference between mass defect and binding energy. (2 marks)
1. Calculate the binding energy per nucleon for Oxygen-16 given: $m_O = 15.99491$ u. (4 marks)
1. Why does fusion require extremely high temperatures? (2 marks)
1. Explain the role of the moderator and control rods in a nuclear reactor. (4 marks)
Answers
1. Mass defect is the difference in mass between individual nucleons and the assembled nucleus. Binding energy is the energy equivalent of this mass difference ( $E = \Delta mc^2$ ).

Want to check your answers and get step-by-step solutions?

Summary

$E = mc^2$ ; mass defect → binding energy
BE per nucleon peaks at Fe-56 (most stable)
Fission: heavy → lighter nuclei + neutrons + energy
Fusion: light → heavier nucleus + energy
Both move towards higher BE per nucleon (Fe-56)

Tags:

#a-level#physics#nuclear#fission#fusion#binding-energy#mass-defect#e-mc2

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