Radio carbon dating calculations
Further complications arise when the carbon in a sample has not taken a straightforward route from the atmosphere to the organism and thence to the measured sample. As soon as a living organism dies, it stops taking in new carbon.Plants and animals assimilate carbon 14 from carbon dioxide throughout their lifetimes.When they die, they stop exchanging carbon with the biosphere and their carbon 14 content then starts to decrease at a rate determined by the law of radioactive decay.For radiocarbon dating to be possible, the material must once have been part of a living organism.This means that things like stone, metal and pottery cannot usually be directly dated by this means unless there is some organic material embedded or left as a residue.Obviously there will usually be a loss of stable carbon too but the proportion of radiocarbon to stable carbon will reduce according to the exponential decay law: R = A exp(-T/8033) where R is C ratio of the living organism and T is the amount of time that has passed since the death of the organism.By measuring the ratio, R, in a sample we can then calculate the age of the sample: T = -8033 ln(R/A) Both of these complications are dealt with by calibration of the radiocarbon dates against material of known age.
Because the radiocarbon is radioactive, it will slowly decay away.
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.
It must be noted though that radiocarbon dating results indicate when the organism was alive but not when a material from that organism was used.
There are three principal techniques used to measure carbon 14 content of any given sample— gas proportional counting, liquid scintillation counting, and accelerator mass spectrometry.