See also: socratic.org/questions/carbon-14-has-a-half-life-of-5714-years-how-many-years-old-is-an-artifact-that-c
Cosmic rays hitting Nitrogen (#""^14"N"#) in the upper atmosphere can convert it into carbon-14 (#""^14"C"#) which is an unstable form of carbon, with a half life of about #5700# years. The tiny ratio of #""^14"C"# to #""^12"C"# is reasonably stable, though slightly variable.
The #""^14"C"# is chemically identical to normal #""^12"C"#, so while an animal or plant is living it get incorporated into organic material (bone, wood, etc) in the same proportion that it occurs in the atmosphere. When the animal or plant dies, it stops absorbing carbon from the atmosphere and the proportion of #""^14"C"# to #""^12"C"# in bone, wood, etc starts decreasing in accordance with the half life of #""^14"C"#.
So by measuring the proportion of #""^14"C"# to #""^12"C"# in a piece of organic material, you can calculate how many years have elapsed since the animal or plant died.
