In mathematical terms, radioactive decay is governed by a simple exponential formula, taught in many high school math classes: P is the amount after time t, and L is the decay constant for the radioactive isotope.This decay constant L can be expressed in terms of the half life T (the time it takes for one-half of the material to decay) as L = log(2) / T, where log(2) = 0.693147... In other words, if we know P, or even merely their ratio, we can solve the above equation for the time t.
Radiometric dating is rooted in the rates of radioactive decay of various isotopes, which rates have been measured carefully in numerous laboratories beginning in the early 20th century.
Radioactive decay is in turn a very basic physical phenomenon, well understood as a consequence of quantum mechanics.
The corresponding dates obtained from these isochrons (based on the slopes of the lines), together with statistical standard deviations, are: 4.396 ± 0.18, 3.673 ± 0.014, 2.991 ± 0.15, and 4.478 ± 0.034 (each figure is in billions of years). But with the advent of mass spectrometry beginning in the 1970s, even very small samples can now be accurately dated.
For example, the "SHRIMP" ion microprobe now in use in numerous laboratories around the world can reliably measure U-Pb and Pb-Pb ages from spots only 0.02 mm (i.e., 20 micrometers) in size within a zircon crystal [Dalrymple2004, pg. It should be emphasized, though, that even relatively unsophisticated equipment can perform radiometric measurements of dates fairly well.
The half-life T of this decay has been measured in careful laboratory measurements as T = 48.8 billion years.
On the other hand, strontium-86 is a stable isotope.
Con All radioactive dating except Carbon 14 are based on atoms found in igneous rocks. So radioactive dating can be used to directly date fossils. However Carbon 14 has a relatively short half life so it cannot be used on fossils much older than 50,000 years which makes it useful for anthropology but not geo history.
Also most fossils no longer contain Carbon they have been turned to stone.
Note how breathtakingly close these points are to the fitted lines (thus confirming with high statistical confidence the validity of the resulting dates): The data for the first graph (upper left) is a set of measurements of basaltic achondrites (meteorites) in [Basaltic1981, pg.