A particular isotope of a particular element is called a nuclide. That is, at some point in time, an atom of such a nuclide will undergo radioactive decay and spontaneously transform into a different nuclide.
This transformation may be accomplished in a number of different ways, including alpha decay (emission of alpha particles) and beta decay (electron emission, positron emission, or electron capture).
This predictability allows the relative abundances of related nuclides to be used as a clock to measure the time from the incorporation of the original nuclides into a material to the present.
The basic equation of radiometric dating requires that neither the parent nuclide nor the daughter product can enter or leave the material after its formation.
In these cases, usually the half-life of interest in radiometric dating is the longest one in the chain, which is the rate-limiting factor in the ultimate transformation of the radioactive nuclide into its stable daughter.
Isotopic systems that have been exploited for radiometric dating have half-lives ranging from only about 10 years (e.g., tritium) to over 100 billion years (e.g., samarium-147).
All ordinary matter is made up of combinations of chemical elements, each with its own atomic number, indicating the number of protons in the atomic nucleus.
Additionally, elements may exist in different isotopes, with each isotope of an element differing in the number of neutrons in the nucleus.
As the mineral cools, the crystal structure begins to form and diffusion of isotopes is less easy.
At a certain temperature, the crystal structure has formed sufficiently to prevent diffusion of isotopes.
Another possibility is spontaneous fission into two or more nuclides.