Nuclear Fission and Fusion

$\text{Nuclear fission}$ is the splitting of a heavy nucleus into two smaller daughter nuclei (plus, typically, a few free neutrons and energy). Because heavy nuclei sit on the right-hand, downward-sloping side of the binding energy per nucleon curve, splitting one into two medium-sized nuclei — each with higher binding energy per nucleon, closer to the peak — releases the difference as energy.

$\text{Induced fission}$ happens when a heavy, fissile nucleus (such as uranium-235) absorbs a slow-moving neutron, becomes highly unstable, and splits apart. Crucially, each fission releases 2–3 new free neutrons, which can go on to induce fission in further nuclei — a self-sustaining $\text{chain reaction}$, the basis of both nuclear reactors and fission weapons.

For a chain reaction to be self-sustaining, on average at least one neutron from each fission event must go on to cause another fission — this depends on having enough fissile material present. The $\text{critical mass}$ is the minimum mass of fissile material needed to sustain a chain reaction: below it (subcritical), too many neutrons escape or are absorbed without effect and the reaction dies out; above it (supercritical), the reaction rate increases uncontrollably.

In a nuclear reactor, the reaction is kept exactly $\text{critical}$ — a steady, controlled rate — using two key components. A $\text{moderator}$ (such as graphite or water) slows fast neutrons released by fission down to much slower "thermal" speeds, since slow neutrons are far more likely to cause further fission in uranium-235. $\text{Control rods}$ (made of a strongly neutron-absorbing material such as boron or cadmium) can be inserted or withdrawn to absorb excess neutrons, precisely controlling the reaction rate.

$\text{Nuclear fusion}$ is the joining of two light nuclei to form a single, heavier nucleus. Light nuclei sit on the steeply-rising, left-hand side of the binding energy per nucleon curve, so fusing them into a heavier nucleus (still lighter than iron) moves the product closer to the stability peak, again releasing energy — in fact, fusion releases considerably more energy per unit mass of fuel than fission does, which is why it powers every star, including the Sun.

For two nuclei to fuse, the strong nuclear force must be able to act between them — but that force only has a very short range, so the nuclei must first get extremely close together. Since every nucleus carries positive charge, they strongly repel each other electrostatically (the $\text{Coulomb barrier}$) at any larger separation, and this repulsion must be overcome by giving the nuclei enormous kinetic energy before they can ever get close enough for the strong force to take over.

This is precisely why fusion requires temperatures of many millions of kelvin (giving nuclei enough average kinetic energy, via $\frac{3}{2}kT$, to occasionally overcome the Coulomb barrier) — conditions that occur naturally in the cores of stars, but which are extremely difficult to create and, especially, to sustain in a controlled way on Earth. This is the central engineering challenge that has so far prevented controlled nuclear fusion from becoming a practical power source.