In order to use radiometric dating processes we must understand the rate at which unstable isotopes decay as well as how the isotope becomes incorporated in the material being dated. Each unstable isotope has its own decay rate known as its half life. The half life of an isotope simply represent the time it takes for one half of a given number of parent isotopes to decay to a stable daughter isotope. For example starting with 100% of a parent isotope after one half-life only 50% of the parent isotope would remain, after a second half-life half of the remaining parent isotopes would have also decayed leaving only 25% of the original parent isotope and 75% daughter isotope. Through chemical analysis it is possible to measure the percent parent and daughter isotopes present in a given material and thereby determine the number of half-lives that have passed since the parent isotope was incorporated within the material. To determine the age of an event we simply multiply the time contained within each half life by the number of half-lives that have passed.
Depending on the parent isotope half lives can vary from 1/billionth of a second to 49 billion years. As the parent isotope decays and as long as the material being dated is in a closed system (meaning no material was able to escape or enter) the amount of parent isotope will continue to decrease while the amount of daughter isotope will continue to increase. If the material being tested was not a closed system and parent or daughter isotopes were able to migrate through the material radiometric dating would yield an inaccurate age. It is for this reason that geologist must take care to ensure that a material was unaltered before radiometrically dating.
Example: analysis of a quartz crystal shows it to contain 25% Uranium 235 and 75% Lead 207. If the half life of Uranium 235 is 704 million years how old is the quartz crystal? Assuming that at the time of crystallization the quartz crystal only contained uranium 235 than it would have taken two half-lives for the uranium to decrease to 25%. The age of the crystal is then 2 X 704 million years or 1,408,000,000 years old.