Decay chain

In nuclear science a decay chain refers to the predictable series of radioactive disintegrations undergone by the nuclei of certain unstable chemical elements.

Radioactive isotopes do not usually decay directly to stable isotopes, but rather into another radioisotope. The isotope produced by this radioactive emission then decays into another, often radioactive isotope. This chain of decays always terminates in a stable isotope, whose nucleus no longer has the surplus of energy necessary to produce another emission of radiation. Such stable isotopes are then said to have reached their ground states.

The stages or steps in a decay chain are referred to by their relationship to previous or subsequent stages. Hence, a parent isotope is one that undergoes decay to form a daughter isotope. For example element 92, uranium, has an isotope with 144 neutrons (²³⁶U) and it decays into an isotope of element 90, thorium, with 142 neutrons (²³²Th). The daughter isotope may be stable or it may itself decay to form another daughter isotope. ²³²Th does this when it decays into radium-228. The daughter of a daughter isotope, such as ²²⁸Ra, is sometimes called a granddaughter isotope. ²²⁸Ra in turn undergoes a further eight decays and transmutations until a stable isotope, ²⁰⁸Pb, is produced, terminating the decay chain of ²³⁶U.

The time required for an atom of a parent isotope to decay into its daughter is fundamentally unpredictable and varies widely. For individual nuclei the process is not known to have determinable causes and the time at which it occurs is therefore completely random. The only prediction that can be made is statistical and expresses an average rate of decay. This rate can be represented by adjusting the curve of a decaying exponential distribution with a decay constant (λ) particular to the isotope. On this understanding the radioactive decay of an initial population of unstable atoms over time t follows the curve given by e^−λt.

One of the most important properties of any radioactive material follows from this analysis, its half-life. This refers to the time required for half of a given number of radioactive atoms to decay and is inversely related to the isotope's decay constant, λ. Half-lives have been determined in laboratories for many radionuclides, and can range from nearly instantaneous—hydrogen-5 decays in less time than it takes for a photon to go from one end of its nucleus to the other—to fourteen orders of magnitude longer than the age of the universe: tellurium-128 has a half-life of 2.2×10²⁴ years.

The Bateman equation predicts the relative quantities of all the isotopes that compose a given decay chain once that decay chain has proceeded long enough for some of its daughter products to have reached the stable (i.e., nonradioactive) end of the chain. A decay chain that has reached this state, which may require billions of years, is said to be in equilibrium. A sample of radioactive material in equilibrium produces a steady and steadily decreasing quantity of radioactivity as the isotopes that compose it traverse the decay chain. On the other hand, if a sample of radioactive material has been isotopically enriched, meaning that a radioisotope is present in larger quantities than would exist if a decay chain were the only cause of its presence, that sample is said to be out of equilibrium. An unintuitive consequence of this disequilibrium is that a sample of enriched material may occasionally increase in radioactivity as daughter products that are more highly radioactive than their parents accumulate. Both enriched and depleted uranium provide examples of this phenomenon.

The chemical elements came into being in two phases. The first commenced shortly after the Big Bang. From ten seconds to 20 minutes after the beginning of the universe the earliest condensation of light atoms was responsible for the manufacture of the four lightest elements. The vast majority of this primordial production consisted of the three lightest isotopes of hydrogen—protium, deuterium and tritium—and two of the nine known isotopes of helium—helium-3 and helium-4. Trace amounts of lithium-7 and beryllium-7 were likely also produced.

So far as is known, all heavier elements came into being starting around 100 million years later, in a second phase of nucleosynthesis that commenced with the birth of the first stars. The nuclear furnaces that power stellar evolution were necessary to create large quantities of all elements heavier than helium, and the r- and s-processes of neutron capture that occur in stellar cores are thought to have created all such elements up to iron and nickel (atomic numbers 26 and 28). The extreme conditions that attend supernovae explosions are capable of creating the elements between oxygen and rubidium (i.e., atomic numbers 8 through 37). The creation of heavier elements, including those without stable isotopes—all elements with atomic numbers greater than lead's, 82—appears to rely on r-process nucleosynthesis operating amid the immense concentrations of free neutrons released during neutron star mergers.