What is the formula for carbon dating?

Answer 1

Carbon radiometric dating is based on measuring the amount of carbon-14 isotope in a sample of carbon of organic origin (from a living thing that is now dead). In a living thing the amount of carbon-14 in its carbon remains at equilibrium with its environment (~1.5 PPB) which remains roughly constant due to the production of carbon-14 by cosmic ray impacts with atoms in the upper atmosphere. This carbon-14 is continuously decaying by beta decay to nitrogen-14, but by interconnection with its environment the lost carbon-14 is replaced.

Once the living thing dies however it is no longer interconnected to its environment and the decayed carbon-14 is no longer replaced. Carbon-14 decays with a halflife of 5730 years. By measuring the amount of carbon-14 in the sample and calculating how long on the exponential curve it took to drop from the equilibrium level it had when last alive to its current measured level, you get the age of the sample.

The technique is not perfect:

1. for a variety of reasons the carbon-14 level in the environment is not actually constant over time, this requires checking carbon dating ages against other dating methods ages in many cases
2. materials older than about 40000 to 50000 years old are usually not datable with carbon dating as the level of carbon-14 in the sample has decayed to low to be reliably measured with any accuracy
3. of course it will not work on samples that do not contain carbon or which are contaminated with either carbon of nonorganic origin or ancient organic carbon (carbon in which all the carbon-14 has already decayed)
4. etc.