AQA AQA 2018-style practice: A nuclear reaction has a mass defect of 0.185 u. Calculate the energy released, in joules. Take 1 u = 1.66 × 10^-27 kg and c = 3.00 × 10^8 m s^-1.

Convert the mass defect to kilograms: m = 0.185 × 1.66 × 10^-27 = 3.07 × 10^-28 kg. Use E = m c^2 = (3.07 × 10^-28)(3.00 × 10^8)^2 = (3.07 × 10^-28)(9.00 × 10^16). E = 2.76 × 10^-11 J (equivalently 0.185 × 931.5 = 172 MeV). Markers reward converting u to kg, squaring the speed of light, and the correct energy. A common slip is to forget to square c.

EnglandPhysicsSyllabus dot point

Where does the enormous energy of nuclear reactions come from?

Mass and energy equivalence, mass defect and binding energy, the binding energy per nucleon curve, and the energy released in fission and fusion.

A focused answer to AQA A-Level Physics 3.8.1.7 and 3.8.1.8, covering mass and energy equivalence, mass defect, binding energy and binding energy per nucleon, the binding energy curve, and the energy released in nuclear fission and fusion.

Generated by Claude Opus 4.810 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Mass and energy equivalence
Mass defect and binding energy
Binding energy per nucleon
Energy from fission and fusion
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What this dot point is asking

AQA specification points 3.8.1.7 and 3.8.1.8 want you to use mass and energy equivalence, define mass defect and binding energy, interpret the binding energy per nucleon curve, and use it to explain the energy released in fission and fusion.

Mass and energy equivalence

Einstein's relation tells us that mass is a form of energy, so the two are not separately conserved but together form a conserved quantity. The factor $c^2$ is huge, which is why a tiny mass defect releases an enormous energy: this is why nuclear reactions release millions of times more energy per atom than chemical reactions, which involve no measurable mass change.

Mass defect and binding energy

When nucleons come together to form a nucleus, energy is released (the binding energy), and by mass-energy equivalence this lost energy corresponds to the lost mass, the mass defect. The assembled nucleus is therefore lighter than its parts, and the missing mass is a direct measure of how strongly the nucleus is bound.

Binding energy per nucleon

The total binding energy increases with size, but the per-nucleon value is what tells you about stability, and it is the quantity used to predict whether a reaction releases energy.

Energy from fission and fusion

Fusion releases more energy per nucleon than fission because the left side of the curve is much steeper, which is why the Sun (powered by hydrogen fusion) is so energetic.

Calculating the energy released from a mass defect

A nuclear reaction has a mass defect of $0.20 \text{ u}$ . Find the energy released in MeV and in joules. Take $1 \text{ u} = 931.5 \text{ MeV} = 1.66 \times 10^{-27} \text{ kg}$ .

step 1: Use the u-to-MeV conversion

$E = 0.20 \times 931.5 = 186 \text{ MeV}$ .

step 2: Convert the mass defect to kilograms

$\Delta m = 0.20 \times 1.66 \times 10^{-27} = 3.32 \times 10^{-28} \text{ kg}$ .

step 3: Apply $E = \Delta m c^2$

$E = (3.32 \times 10^{-28})(3.00 \times 10^8)^2 = (3.32 \times 10^{-28})(9.00 \times 10^{16})$ .

step 4: Evaluate and check

$E = 2.99 \times 10^{-11} \text{ J}$ , which matches $186 \text{ MeV}$ when converted ( $186 \times 1.6 \times 10^{-13} = 3.0 \times 10^{-11} \text{ J}$ ).

Try this

Q1. Define the binding energy of a nucleus. [1 mark]

Cue. The energy needed to separate a nucleus completely into its individual nucleons.

Q2. State why energy is released when two light nuclei fuse. [1 mark]

Cue. The product nucleus has a higher binding energy per nucleon, so energy is released.

Q3. State which nucleus has the highest binding energy per nucleon. [1 mark]

Cue. Iron-56 (near the peak of the curve).

Exam-style practice questions

Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AQA 20184 marksA nuclear reaction has a mass defect of

0.185 \text{ u}

. Calculate the energy released, in joules. Take

1 \text{ u} = 1.66 \times 10^{-27} \text{ kg}

and

c = 3.00 \times 10^8 \text{ m s}^{-1}

Show worked answer →

Convert the mass defect to kilograms: $\Delta m = 0.185 \times 1.66 \times 10^{-27} = 3.07 \times 10^{-28} \text{ kg}$ .

Use $E = \Delta m c^2 = (3.07 \times 10^{-28})(3.00 \times 10^8)^2 = (3.07 \times 10^{-28})(9.00 \times 10^{16})$ .

$E = 2.76 \times 10^{-11} \text{ J}$ (equivalently $0.185 \times 931.5 = 172 \text{ MeV}$ ).

Markers reward converting u to kg, squaring the speed of light, and the correct energy. A common slip is to forget to square $c$ .

AQA 20214 marksUsing the shape of the binding energy per nucleon curve, explain why energy is released both when heavy nuclei undergo fission and when light nuclei undergo fusion.

Show worked answer →

The binding energy per nucleon rises steeply for light nuclei, peaks near iron-56 (the most stable nucleus), then falls gradually for heavy nuclei. A higher binding energy per nucleon means a more stable nucleus.

In fission, a heavy nucleus (right of the peak) splits into lighter nuclei nearer the peak, which have a higher binding energy per nucleon, so energy is released. In fusion, light nuclei (far left, low binding energy per nucleon) combine to form a nucleus nearer the peak, again with a higher binding energy per nucleon, releasing energy.

In both cases the products are more tightly bound, the total mass decreases, and the lost mass appears as energy via $E = mc^2$ .

Markers reward describing the curve shape and peak, both processes moving towards higher binding energy per nucleon, and linking the mass decrease to released energy.

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Sources & how we know this

AQA A-level Physics (7408) specification — AQA (2017)