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 normally involves isotope-ratio mass spectrometry. The precision of a dating method depends in part on the half-life of the radioactive isotope involved.
Another possibility is spontaneous fission into two or more nuclides.
While the moment in time at which a particular nucleus decays is unpredictable, a collection of atoms of a radioactive nuclide decays exponentially at a rate described by a parameter known as the half-life, usually given in units of years when discussing dating techniques.
After one half-life has elapsed, one half of the atoms of the nuclide in question will have decayed into a "daughter" nuclide or decay product.
In many cases, the daughter nuclide itself is radioactive, resulting in a decay chain, eventually ending with the formation of a stable (nonradioactive) daughter nuclide; each step in such a chain is characterized by a distinct half-life.
The only exceptions are nuclides that decay by the process of electron capture, such as beryllium-7, strontium-85, and zirconium-89, whose decay rate may be affected by local electron density.