dating style games A mathematical explanation of carbon dating and half life

Radioactive decay is a first order rate process, which means the reaction proceeds according to the following equation:log is the quantity of radioactive material at time zero, X is the amount remaining after time t, and k is the first order rate constant, which is a characteristic of the isotope undergoing decay.

A form of radiometric dating used to determine the age of organic remains in ancient objects, such as archaeological specimens, on the basis of the half-life of carbon-14 and a comparison between the ratio of carbon-12 to carbon-14 in a sample of the remains to the known ratio in living organisms. A technique for measuring the age of organic remains based on the rate of decay of carbon 14.

The carbon 14 present in an organism at the time of its death decays at a steady rate, and so the age of the remains can be calculated from the amount of carbon 14 that is left. The cells of all living things contain carbon atoms that they take in from their environment.

Back in the 1940s, the American chemist Willard Libby used this fact to determine the ages of organisms long dead.

Most carbon atoms have six protons and six neutrons in their nuclei and are called carbon 12. But a tiny percentage of carbon is made of carbon 14, or radiocarbon, which has six protons and eight neutrons and is not stable: half of any sample of it decays into other atoms after 5,700 years.

Carbon 14 is continually being created in the Earth's atmosphere by the interaction of nitrogen and gamma rays from outer space.

Since atmospheric carbon 14 arises at about the same rate that the atom decays, the Earth's levels of carbon 14 have remained constant.

In living organisms, which are always taking in carbon, the levels of carbon 14 likewise stay constant.

But in a dead organism, no new carbon is coming in, and its carbon 14 gradually begins to decay.

So by measuring carbon 14 levels in an organism that died long ago, researchers can figure out when it died.

The procedure of radiocarbon dating can be used for remains that are up to 50,000 years old.

Perhaps the most widely used evidence for the Theory of Evolution through Natural Selection is the fossil record.