Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material. The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles. Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon. At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues. 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 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.
Radiometric Age Dating - Geology (U.S. National Park Service)
This is how carbon dating works: Carbon is a naturally abundant element found in the atmosphere, in the earth, in the oceans, and in every living creature. C is by far the most common isotope, while only about one in a trillion carbon atoms is C C is produced in the upper atmosphere when nitrogen N is altered through the effects of cosmic radiation bombardment a proton is displaced by a neutron effectively changing the nitrogen atom into a carbon isotope. The new isotope is called "radiocarbon" because it is radioactive, though it is not dangerous. It is naturally unstable and so it will spontaneously decay back into N after a period of time. It takes about 5, years for half of a sample of radiocarbon to decay back into nitrogen. It takes another 5, for half of the remainder to decay, and then another 5, for half of what's left then to decay and so on.
In this section we will explore the use of carbon dating to determine the age of fossil remains. Carbon is a key element in biologically important molecules. During the lifetime of an organism, carbon is brought into the cell from the environment in the form of either carbon dioxide or carbon-based food molecules such as glucose; then used to build biologically important molecules such as sugars, proteins, fats, and nucleic acids. These molecules are subsequently incorporated into the cells and tissues that make up living things.
This figure is directly based on the proportion of radiocarbon found in the sample. It is calculated on the assumption that the atmospheric radiocarbon concentration has always been the same as it was in and that the half-life of radiocarbon is years. To give an example if a sample is found to have a radiocarbon concentration exactly half of that for material which was modern in the radiocarbon measurement would be reported as BP. In order to see what a radiocarbon determination means in terms of a true age we need to know how the atmospheric concentration has changed with time.