The nuclei of radioactive isotopes are inherently unstable, and will spontaneously decay into chemically distinct daughter isotopes at a fixed rate. Radioactive decay rates are unaffected by any environmental condition such as temperature, moisture, or pressure. Thus, radioactive isotopes work as natural clocks and provide us with an absolute dating method called radiometric dating. Here is how it works:
1. The half-life of the radioactive isotope is experimentally determined by kinetics.
2. The ratio of parent isotope to daughter isotope in a rock is measured, usually by mass spectrometry.
3. The amount of time that has passed since the sample was formed can now be calculated by using the formula
t= 1/(x ln (1+ D/P))
where t= elapsed time D= the present number of atoms of the daughter isotope P= the present number of atoms of the parent isotope, and x = the decay constant, which is related to the half-life T^1/2 by x = 0.693/T^1/2
Key assumptions are that only the parent isotope is present when the rock is formed and that neither parent nor daughter isotopes migrate into or out of the rock after its formation. When these assumptions are met, the procedure is precise and reliable.