The pair of blue curves show the radiocarbon measurements on the tree rings (plus and minus one standard deviation) and the red curve on the left indicates the radiocarbon concentration in the sample.
The grey histogram shows possible ages for the sample (the higher the histogram the more likely that age is).
The first indicates the proportion of radiocarbon atoms in the sample as compared to samples modern in 1950.
The second is directly derived from this on the assumption that the half-life of radiocarbon is 5568 years and the amount of radiocarbon in the atmosphere has been constant.
The wood in these rings once laid down remains unchanged during the life of the tree.
This is very useful as a record of the radiocarbon concentration in the past.
Carbon-14 has a half-life of 5,730 ± 40 years—, half the amount of the radioisotope present at any given time will undergo spontaneous disintegration during the succeeding 5,730 years.
By using these widths, it is possible to compare the tree rings in a dead tree to those in a tree that is still growing in the same region.
Since the calendar age of the tree rings is known, this then tells you the age of your sample.
In practice this is complicated by two factors: These effects are most clearly seen by looking at a specific example.
Carbon-14 is continually formed in nature by the interaction of neutrons with nitrogen-14 in the Earth’s atmosphere; the neutrons required for this reaction are produced by cosmic rays interacting with the atmosphere.
Radiocarbon present in molecules of atmospheric carbon dioxide enters the biological carbon cycle: it is absorbed from the air by green plants and then passed on to animals through the food chain.
Radiocarbon measurements are always reported in terms of years `before present' (BP).