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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.
The 14C formed is rapidly oxidised to 14CO2 and enters the earth's plant and animal lifeways through photosynthesis and the food chain.
The rapidity of the dispersal of C14 into the atmosphere has been demonstrated by measurements of radioactive carbon produced from thermonuclear bomb testing.
Libby and his team intially tested the radiocarbon method on samples from prehistoric Egypt.
It follows from this that any material which is composed of carbon may be dated.
Renfrew (1973) called it 'the radiocarbon revolution' in describing its impact upon the human sciences.