Binding Energy, Fission and Fusion

Mass–energy equivalence — mass and energy are two aspects of the same thing:

E = m c²

Because c² is about 9 × 10¹⁶, a tiny mass corresponds to an enormous energy. One gram is equivalent to roughly 9 × 10¹³ J, comparable to a large power station's daily output.

Mass defect — the mass of a nucleus is always less than the total mass of its separate nucleons. The difference is the mass defect, and its energy equivalent is the binding energy: the energy needed to pull the nucleus completely apart.

Binding energy per nucleon — the binding energy divided by the number of nucleons. This, not the total, is the measure of stability, because it allows nuclei of different sizes to be compared fairly.

The binding energy per nucleon curve — rises steeply from hydrogen, peaks at iron-56 at about 8.8 MeV per nucleon, then falls slowly towards uranium.

Why the peak explains both fission and fusion — any process that moves nuclei towards iron releases energy:

Fusion — joining light nuclei, moving up the left-hand slope. This powers stars, and is the more energetic per nucleon of the two.

Fission — splitting heavy nuclei, moving up the right-hand slope. This is what a nuclear reactor does.

Example: this single curve is one of the most economical pieces of physics in the specification. It explains why the Sun shines, why reactors work, why iron is the end of stellar fusion, and why elements beyond iron must be made in supernovae. One graph, four consequences.

Fission — a heavy nucleus such as uranium-235 absorbs a neutron, becomes unstable and splits into two lighter nuclei plus two or three neutrons. Those neutrons can trigger further fissions — a chain reaction.

Reactor control

Moderator (water or graphite) — slows the neutrons, since slow neutrons are far more likely to be absorbed and cause further fission.

Control rods (boron or cadmium) — absorb neutrons, and are raised or lowered to hold the reaction exactly critical.

Coolant — carries the heat away to generate steam.

Fusion requires enormous temperatures, of order 10⁷ K, so that nuclei approach fast enough to overcome their electrostatic repulsion and come within range of the strong nuclear force. That requirement, not the physics of the reaction, is what makes sustained fusion power so difficult on Earth.