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Where does nuclear energy come from, and why do both fission and fusion release it?

Mass-energy equivalence, the mass defect and binding energy, binding energy per nucleon, and nuclear fission and fusion.

A focused answer to WJEC A-Level Physics Unit 3 nuclear energy, covering mass-energy equivalence, the mass defect and binding energy, the binding energy per nucleon curve, and why both nuclear fission and fusion release energy.

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  1. What this dot point is asking
  2. The answer
  3. Examples in context
  4. Try this

What this dot point is asking

WJEC wants you to use mass-energy equivalence, explain the mass defect and binding energy, interpret the binding energy per nucleon curve, and explain why both fission and fusion release energy. This dot point ties together E=mc2E = mc^2, the structure of the nucleus and the physics of reactors and stars, and the binding-energy curve is one of the most important graphs in the whole specification.

The answer

Mass-energy equivalence

Mass and energy are equivalent; a change in mass Δm\Delta m corresponds to an energy ΔE=Δm c2\Delta E = \Delta m\, c^2. Because c2c^2 is so large, even a tiny mass change releases an enormous amount of energy, which is why nuclear reactions dwarf chemical ones.

Mass defect and binding energy

Binding energy per nucleon

Fission and fusion

Fission splits a very heavy nucleus (such as uranium-235) into two lighter nuclei, which lie closer to the peak, so the binding energy per nucleon increases and energy is released. Fusion joins light nuclei (such as hydrogen isotopes) into a heavier one, also moving up the steep early part of the curve, releasing even more energy per nucleon, and powering stars.

Examples in context

Example 1. A nuclear power station. In a fission reactor, uranium-235 absorbs a neutron and splits, releasing about 200 MeV200\,\text{MeV} per fission as kinetic energy of the fragments. This energy heats water into steam, which drives a turbine. A tiny mass defect, multiplied by the huge c2c^2, is what lets a few kilograms of fuel power a city.

Example 2. The Sun. In the Sun's core, hydrogen nuclei fuse into helium, converting about 0.7%0.7\% of the mass into energy via E=mc2E = mc^2. This fusion releases the radiation that warms the Earth and has sustained the Sun for billions of years. Recreating controlled fusion on Earth is the goal of reactors like the tokamak, which aim to climb the same steep left-hand side of the binding-energy curve.

Try this

Q1. A nuclear reaction has a mass defect of 3.0×10−29 kg3.0\times10^{-29}\,\text{kg}. Find the energy released. Take c=3.0×108 m s−1c = 3.0\times10^8\,\text{m s}^{-1}. [2 marks]

  • Cue. E=mc2=3.0×10−29×(3.0×108)2=2.7×10−12 JE = mc^2 = 3.0\times10^{-29}\times(3.0\times10^8)^2 = 2.7\times10^{-12}\,\text{J}.

Q2. Explain why fusing two light nuclei releases energy. [2 marks]

  • Cue. The product has a higher binding energy per nucleon, so it is more tightly bound; the difference is released.

Exam-style practice questions

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

WJEC 20196 marksIn a fission reaction the total mass of the products is less than the mass of the reactants by 3.1×10−28 kg3.1 \times 10^{-28}\,\text{kg}. Calculate the energy released in joules and in MeV, and state what becomes of this energy in a reactor. Take c=3.0×108 m s−1c = 3.0 \times 10^{8}\,\text{m s}^{-1} and 1 MeV=1.6×10−13 J1\,\text{MeV} = 1.6 \times 10^{-13}\,\text{J}.
Show worked answer →

Energy released from mass-energy equivalence:

E=Δm c2=3.1×10−28×(3.0×108)2=3.1×10−28×9.0×1016=2.79×10−11 JE = \Delta m\, c^2 = 3.1 \times 10^{-28} \times (3.0 \times 10^{8})^2 = 3.1 \times 10^{-28} \times 9.0 \times 10^{16} = 2.79 \times 10^{-11}\,\text{J}.

In MeV: E=2.79×10−111.6×10−13=174 MeVE = \dfrac{2.79 \times 10^{-11}}{1.6 \times 10^{-13}} = 174\,\text{MeV}.

In a reactor this energy mostly appears as kinetic energy of the fission fragments, which is transferred to the surrounding material as heat. This heat boils water to drive a turbine and generate electricity. Markers reward E=Δmc2E = \Delta m c^2, the conversion to about 174 MeV174\,\text{MeV}, and identifying the energy as heat used to generate electricity.

WJEC 20214 marksUsing the shape of the binding energy per nucleon curve, explain why energy is released both when uranium undergoes fission and when hydrogen isotopes undergo fusion.
Show worked answer →

The binding energy per nucleon curve rises steeply for light nuclei, peaks near iron-56, then falls slowly for heavy nuclei. A higher binding energy per nucleon means a more stable, more tightly bound nucleus.

Uranium lies on the falling right-hand side of the curve. Splitting it into two medium-mass fragments moves those nucleons up toward the peak, increasing the binding energy per nucleon, and the difference is released as energy.

Hydrogen isotopes lie on the steep left-hand side. Fusing them into helium moves the nucleons up the steep rise toward the peak, a large increase in binding energy per nucleon, releasing even more energy per nucleon than fission. In both cases nucleons end up more tightly bound, so energy is released. Markers reward referring to movement toward the peak and the increase in binding energy per nucleon for both processes.

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