The Quantum Physics Concept Of Critical Mass

In the sub-atomic realm governed by the rules of quantum mechanics, a process called fission provides the fundamental source of energy for both atom bombs and nuclear reactors. What separates these two vastly different results — one violent, the other controlled — is the concept of critical mass, an imaginary dividing line that determines whether a nuclear reaction is slow and prolonged or rapid and short-lived.

Atoms of unstable elements such as uranium and plutonium split into pairs of lighter elements when they undergo radioactive decay, a process called fission. For example, uranium-235 may split into krypton-89 and barium-144, a fission that also emits two leftover neutrons. The lighter elements may also be unstable, continuing as a radioactive decay chain that may include a dozen or more elements and take millions of years to complete.

A uranium nucleus splits into two lighter elements when it absorbs a stray neutron; the neutron destabilizes the nucleus, making it more likely to undergo a fission. Because a fission produces free neutrons, they may strike neighboring atoms, causing them to also split, creating a chain reaction of fission events. As nuclear reactions are quantum mechanical in nature, they are ruled by probabilities and chance. When chain reactions are less likely to occur, they die out, as fewer and fewer neutrons trigger successive fissions. When circumstances favor chain reactions, fissions continue in a steady fashion. And when fissions are very likely, chain reactions accelerate, splitting a rapidly-increasing number of atoms and releasing their energy.

The likelihood of fissions and chain reactions depends partly on the mass of the radioactive material involved. At a point called critical mass, the chain reactions are largely self-sustaining but not increasing. Each radioactive element has a specific critical mass for a sphere of the substance; for example, the critical mass of uranium-235 is 56 kg, whereas only 11 kg of plutonium-239 is required. Scientists who maintain stockpiles of radioactive materials store them in such a way that these quantities never occur in the same general vicinity; otherwise, they may produce violent bursts of lethal radiation.

For a spherical shape of radioactive substance, increasing the mass increases the number of neutrons given off at a given moment and the likelihood that fissions lead to chain reactions. Quantities smaller than a critical mass of a radioactive element have chain reactions but they are more likely to die out than continue. Beyond the critical mass, the rate of fissions increases, leading to a dangerous, out-of-control situation. Nuclear power plants use sub-critical amounts of radioactive elements — enough to produce generous amounts of power but which, for safety reasons, can never lead to a nuclear explosion. Atom bombs, by contrast, use a quantity of materials much closer to a critical mass. An atom bomb remains sub-critical until it is triggered with a burst of neutrons and squeezed by a blast of conventional high explosives. The explosives cause the material to become momentarily supercritical; chain reactions become out of control in a few millionths of a second, releasing the energy equivalent of tens of thousands of tons of TNT.