The key is to measure an isotope that has had time to decay a measurable amount, but not so much as to only leave a trace remaining.
Given isotopes are useful for dating over a range from a fraction of their half life to about four or five times their half life.
Some isotopes have half lives longer than the present age of the universe, but they are still subject to the same laws of quantum physics and will eventually decay, even if doing so at a time when all remaining atoms in the universe are separated by astronomical distances.
Various elements are used for dating different time periods; ones with relatively short half-lives like carbon-14 (or C) are useful for dating once-living objects (since they include atmospheric carbon from when they were alive) from about ten to fifty thousand years old. Longer-lived isotopes provide dating information for much older times.
This allows the dating of much older and smaller samples but at a far higher cost.
Over the second half-life, of the atoms remaining decay, which leaves of the original quantity, and so on.
In other words, the change in numbers of atoms follows a geometric scale as illustrated by the graph below.other carbon isotopes in the same ratio as exists in the atmosphere.
decay or the rate of other cumulative changes in atoms resulting from radioactivity. The various isotopes of the same element differ in terms of atomic mass but have the same atomic number..
One half-life is the amount of time required for of the original atoms in a sample to decay.