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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.
They chose samples whose age could be independently determined.
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.
A sample of acacia wood from the tomb of the pharoah Zoser (or Djoser; 3rd Dynasty, ca. Libby reasoned that since the half-life of C years, they should obtain a C14 concentration of about 50% that which was found in living wood (see Libby, 1949 for further details).
The results they obtained indicated this was the case.