The methods work because radioactive elements are unstable, and they are always trying to move to a more stable state. This process by which an unstable atomic nucleus loses energy by releasing radiation is called radioactive decay.
The thing that makes this decay process so valuable for determining the age of an object is that each radioactive isotope decays at its own fixed rate, which is expressed in terms of its half-life.
For example, uranium-lead dating can be used to find the age of a uranium-containing mineral.
It works because we know the fixed radioactive decay rates of uranium-238, which decays to lead-206, and for uranium-235, which decays to lead-207.
So, we start out with two isotopes of uranium that are unstable and radioactive.
When the isotope is halfway to that point, it has reached its half-life.
So, if you know the radioactive isotope found in a substance and the isotope's half-life, you can calculate the age of the substance. Well, a simple explanation is that it is the time required for a quantity to fall to half of its starting value.So, you might say that the 'full-life' of a radioactive isotope ends when it has given off all of its radiation and reaches a point of being non-radioactive.