Technology involved in carbon dating
There is a quantitative relationship between the decay of 14C and the production of a beta particle. That is, the probability of decay for an atom of 14C in a discrete sample is constant, thereby requiring the application of statistical methods for the analysis of counting data.
It follows from this that any material which is composed of carbon may be dated.
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).
"Everything which has come down to us from heathendom is wrapped in a thick fog; it belongs to a space of time we cannot measure.
We know that it is older than Christendom, but whether by a couple of years or a couple of centuries, or even by more than a millenium, we can do no more than guess." [Rasmus Nyerup, (Danish antiquarian), 1802 (in Trigger, 19)].
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).
They exist in equilibrium with the C14 concentration of the atmosphere, that is, the numbers of C14 atoms and non-radioactive carbon atoms stays approximately the same over time.
As soon as a plant or animal dies, they cease the metabolic function of carbon uptake; there is no replenishment of radioactive carbon, only decay.
These isotopes are present in the following amounts C12 - 98.89%, C13 - 1.11% and C14 - 0.00000000010%.