The radiocarbon method is based on the rate of decay of the radioactive or unstable carbon isotope 14 (14C), which is formed in the upper atmosphere through the effect of cosmic ray neutrons upon nitrogen 14.
The reaction is: (Where n is a neutron and p is a proton).
The half-life () is the name given to this value which Libby measured at 556830 years. After 10 half-lives, there is a very small amount of radioactive carbon present in a sample.
At about 50 - 60 000 years, then, the limit of the technique is reached (beyond this time, other radiometric techniques must be used for dating).
The 14C formed is rapidly oxidised to 14CO2 and enters the earth's plant and animal lifeways through photosynthesis and the food chain.
Today, there are over 130 radiocarbon dating laboratories around the world producing radiocarbon assays for the scientific community.
There is a useful diagrammatic representation of this process given here Libby, Anderson and Arnold (1949) were the first to measure the rate of this decay.
They found that after 5568 years, half the C14 in the original sample will have decayed and after another 5568 years, half of that remaining material will have decayed, and so on (see figure 1 below).
These isotopes are present in the following amounts C12 - 98.89%, C13 - 1.11% and C14 - 0.00000000010%.
Thus, one carbon 14 atom exists in nature for every 1,000,000,000,000 C12 atoms in living material.