Nuclear Binding Energy and Mass Defect: GCSE Physics

Inside every nucleus, protons and neutrons are held together against enormous electrostatic repulsion by the strong nuclear force. The energy needed to pull a nucleus completely apart is called binding energy — and when nuclei rearrange through fission or fusion, any increase in binding energy is released as heat and radiation, powering both nuclear reactors and stars.

What holds a nucleus together?

A nucleus contains protons (positively charged) and neutrons (neutral). Protons repel each other strongly — the electrostatic (Coulomb) repulsion between two protons at nuclear distances is enormous. Yet most nuclei are stable.

The strong nuclear force holds them together. It:

• Acts between any two nucleons (protons or neutrons) that are close enough
• Is very short-range (effective only up to about 3 × 10⁻¹⁵ m)
• Is attractive at distances of 1–3 fm and repulsive at very short range

For small nuclei the strong force dominates repulsion easily. As nuclei grow larger, the electrostatic repulsion between the increasing number of protons becomes significant, which is why very heavy nuclei (above lead, Z = 82) are all unstable.

What is nuclear binding energy?

Binding energy is the minimum energy required to completely separate all the nucleons in a nucleus into individual free protons and neutrons.

It can also be thought of as the energy released when individual protons and neutrons come together to form the nucleus. The bound nucleus has less energy than the separated nucleons — this energy difference was released when the nucleus formed.

A nucleus with a higher binding energy is more stable: more energy must be supplied to break it apart.

What is mass defect?

When nucleons combine into a nucleus, the nucleus is slightly less massive than the sum of the individual nucleon masses. This missing mass is the mass defect (Δm).

Einstein's mass-energy equivalence explains where the mass goes:

E = mc²

where E is the binding energy, m is the mass defect, and c is the speed of light (3 × 10⁸ m/s).

Example — helium-4 (²He):

(u = unified atomic mass unit = 1.66 × 10⁻²⁷ kg)

The binding energy of helium-4 = Δm × c² = 0.0305 × 1.66 × 10⁻²⁷ × (3 × 10⁸)² ≈ 4.5 × 10⁻¹² J (28.3 MeV)

This is the energy that holds the helium nucleus together, and the energy that would be released if four free nucleons fused to form it.

What is binding energy per nucleon?

Comparing binding energies of different nuclei directly is misleading because larger nuclei have more nucleons. The useful quantity is binding energy per nucleon (BE/A):

BE/A = total binding energy / number of nucleons (A)

A higher BE/A means more stable (each nucleon is more tightly bound).

Key values:

Why does fission release energy?

Nuclear fission splits a heavy nucleus (e.g. uranium-235) into two medium-sized fragments plus neutrons:

²³⁵U + n → ⁹²Kr + ¹⁴¹Ba + 3n + energy

Uranium-235 has a BE/A of about 7.6 MeV/nucleon. The fission products (krypton and barium, near the middle of the periodic table) have BE/A values closer to iron's maximum of 8.8 MeV/nucleon.

Because the products are more tightly bound per nucleon than the original uranium, energy is released — the amount equals the gain in total binding energy. Fission of one uranium-235 nucleus releases about 200 MeV (~3.2 × 10⁻¹¹ J), roughly 50 million times more energy than burning one molecule of methane.

Why does fusion also release energy?

Nuclear fusion joins light nuclei (e.g. hydrogen isotopes) to form heavier ones:

²H + ³H → ⁴He + n + energy (17.6 MeV)

Hydrogen isotopes (deuterium, tritium) have low BE/A. Helium-4 has a much higher BE/A (~7.1 MeV). The fused product is more tightly bound, so energy is released. Fusion releases more energy per kilogram of fuel than fission, and the fuel (hydrogen isotopes) is more abundant — but achieving the 100 million °C temperatures needed for fusion on Earth is the technological challenge facing nuclear fusion reactors.

Frequently asked questions

Why is iron the most stable nucleus?

Iron-56 has the highest binding energy per nucleon of any nucleus — about 8.8 MeV per nucleon. This means that starting from iron and trying to gain energy by fusion (going to heavier nuclei) or by fission (splitting it into lighter ones) is not possible — both processes would require energy input rather than releasing it. Iron is, in a sense, the "dead end" of nuclear energy release. Stars convert lighter elements up to iron via fusion; elements heavier than iron can only be made in the extreme conditions of supernova explosions.

Does E = mc² mean that matter can be converted into energy?

Yes — in nuclear reactions, a small amount of mass genuinely disappears and its equivalent energy is released. The mass defect is real missing mass, not a measurement error. The equivalence E = mc² was proposed by Einstein in 1905 and confirmed experimentally many times, most dramatically by the enormous energy release from nuclear weapons and reactors from far smaller mass changes than any chemical reaction could produce. The factor c² (9 × 10¹⁶ m²/s²) is so large that even tiny mass defects correspond to enormous energy.

Why does fission produce dangerous radiation?

The fission products (daughter nuclei) are typically neutron-rich — they have too many neutrons relative to protons for stability. These unstable nuclei undergo beta decay and emit gamma radiation as they rearrange towards more stable configurations. The neutrons released in each fission event can trigger further fissions (a chain reaction), releasing more gamma radiation and fast neutrons. It is the energetic gamma rays and fast neutrons, plus the radioactive decay of fission products, that create the radiation hazard from nuclear reactors and fallout.

How is binding energy different from ionisation energy?

Binding energy (in the nuclear context) refers to the energy holding nucleons together in a nucleus, involving the strong nuclear force — energies of order MeV (millions of electron-volts). Ionisation energy is the energy needed to remove an electron from an atom, involving electrostatic attraction between the nucleus and electrons — energies of order eV (electron-volts). Nuclear binding energies are roughly a million times larger than ionisation energies, which is why nuclear reactions release so much more energy per atom than chemical reactions.

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