C13 carbon dating
So when we find a sample of organic material and we want to know how old it is, we measure the ratio of C-14/C-12 in the sample.
Carbon-14 is not stable against beta-minus decay with a half-life of 5,730±40 years, but is constantly replenished in the atmosphere by cosmic ray interaction with nitrogen-14.The naturally occurring ratio of C-14/C-12 is about 10^-12 (0.000000000001).After a living organism dies, the carbon-14 in the organism will decay away, but it is no longer replenished by intake by breathing or eating. If any chemical or mechanical processes remove carbon from the dead organism, all carbon will be equally affected so the ratio is unaffected.We can measure the C-14/C-12 ratio in the tree rings.
We can count the rings to see how old the ring is to a very high precision.
After about ten half-lives there is so little C-14 left that dating is impossible.