The age of the rock can be calculated if the ratio of uranium to lead is known.
As the rock gets older the proportion of lead increases.
The ratio of carbon-12 to carbon-14 at the moment of death is the same as every other living thing, but the carbon-14 decays and is not replaced.
The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample.
Plants absorb carbon dioxide from the atmosphere and animals eat plants.
This means all living things have radioactive carbon-14 in them.
When it decays it forms thorium-234 which is also unstable.
Finally, after a series of radioactive isotopes are formed it becomes lead-206, which is stable.
This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50,000 years ago.
When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.
Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.
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.
However, the principle of carbon-14 dating applies to other isotopes as well.