Editing Decay chain (section)

{{Short description|Series of radioactive decays}}
{{Nuclear physics}}

In [[nuclear science]] a '''decay chain''' refers to the predictable series of [[radioactive decay|radioactive disintegration]]s undergone by the nuclei of certain unstable chemical elements. 

[[Radionuclide|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 nuclide|stable isotope]], whose nucleus no longer has the surplus of energy necessary to produce another emission of radiation. Such stable isotopes may be said to have  reached their ''[[Ground state|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 ([[Uranium-236|<sup>236</sup>U]]) and it decays into an isotope of element 90, [[thorium]], with 142 neutrons ([[Isotopes of thorium|<sup>232</sup>Th]]). The daughter isotope may be stable or it may itself decay to form another daughter isotope.  <sup>232</sup>Th does this when it decays into [[Isotopes of radium|radium-228]]. The daughter of a daughter isotope, such as  <sup>228</sup>Ra, is sometimes called a ''granddaughter isotope''.

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 [[Uncertainty principle|not known to have determinable causes]] and the time at which it occurs is therefore [[Poisson point process|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 (mathematical constant)|e]]''<sup>−''λt''</sup>.

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 [[List of radioactive nuclides by half-life|range]] from nearly instantaneous—[[Isotopes of hydrogen|hydrogen-5]] decays in less [[Speed of light|time than it takes]] for a photon to go from one end of its nucleus to the other—to fourteen [[Orders of magnitude (time)|orders of magnitude]] longer than the [[age of the universe]]: [[Isotopes of tellurium|tellurium-128]] has a half-life of {{val|2.2|e=24|u=years}}.

[[File:DecayChain241Pu-eng.svg|thumb|Quantity calculation with the Bateman-Function for <sup>241</sup>Pu]]
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 [[Nuclear enrichment|enriched]] material may occasionally increase in radioactivity as daughter products that are more highly radioactive than their parents accumulate. Both [[Enriched uranium|enriched]] and [[Depleted uranium|depleted]] uranium provide examples of this phenomenon.