Method of dating fossils by radioactive decay
The first is that atoms have always decayed at the same rate.
And this isn’t really an assumption as the decay rates have been tested in the laboratory for a hundred years or so, we have an example of a natural nuclear reactor where we can measure the various products and determine the decay rates (and the fine structure constant), and we can observe the past by looking deep into the past of the universe. The sigh isn’t for the effort of writing, it’s for the effort of finding all the references.
By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely. So, if you had a fossil that had 10 percent carbon-14 compared to a living sample, then that fossil would be: t = [ ln (0.10) / (-0.693) ] x 5,700 years t = [ (-2.303) / (-0.693) ] x 5,700 years t = [ 3.323 ] x 5,700 years Because the half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old.
For organic materials, the comparison is between the current ratio of a radioactive isotope to a stable isotope of the same element and the known ratio of the two isotopes in living organisms.
Radiocarbon dating is one such type of radiometric dating.
For inorganic materials, such as rocks containing the radioactive isotope rubidium, the amount of the isotope in the object is compared to the amount of the isotope's decay products (in this case strontium).
The object's approximate age can then be figured out using the known rate of decay of the isotope.