Radioactive carbon (carbon-14) is formed in the upper atmosphere as a result of bombardment by cosmic rays. These atoms combine with oxygen to form carbon dioxide in a ratio which is nearly constant all over the world. The amount is extremely small, being estimated at one part in a million million (1.85 x 1/1000000000000) gram per gram of carbon-12 (ordinary carbon). From the time a plant or animal dies the radioactivity declines at a rate determined by a law of exponential decay. After 5730 years half of it has gone. After another 5730 years half of what was still left will have died away...and so on. It is therefore only necessary to determine the percentage of carbon-14 remaining to be able to calculate the time since death.
In practice there are several difficulties and the accuracy of the dating depends on several assumptions.
The chief difficulty is the fact that the radioactivity is so very small, especially for old samples, and it must be measured against a background of considerable outside interference. As the upper limit depends on the background interference it varies from laboratory to laboratory but is typically in the region of 40,000 years.
The assumptions necessary for accurate dating are:
1. The atmosphere has had the same carbon-14 concentration in the past as now.
2. After death, the carbon-14 concentration is only affected by radioactive decay.
The problems affecting them are :
1. Production-rate variables affecting the concentration of carbon-14.
(a) Fluctuations in the earth's magnetic field affect carbon-14 production because cosmic rays are deflected by the magnetic field.
(b) Both the production of fossil fuel and the testing of nuclear weapons in modern times has affected the atmospheric content of carbon-14.
2. Processes that change the concentration of carbon-14 in an organism.
(a) Volcanoes issue gases including carbon dioxide. Coming from deep within the earth's crust these have no carbon-14 activity and therefore locally dilute the atmospheric concentration, giving higher apparent ages.
(b) Warm interglacial periods would have released aged carbon (depleted in carbon-14) from the ice masses with the same effect.
3. Contamination by the introduction of extraneous carbon material.
(a) Calcium carbonate such as limestone can dissolve in ground water and be deposited within a sample. Being of geological origin its age would be greatly in excess of the sample.
(b) Contamination from animal glue, conservation chemicals, cigarette ash, paper labels and wrapping paper could make a sample seem older or younger.
Does this mean it doesn't work ? No. When it can be calibrated with other dating methods (e.g. dendrochronology [tree-rings]) it can be very good but it should be treated with increasing caution for very high dates.
Earnest
"Beware the Jubjub bird, and shun the frumious Bandersnatch!" - Rev. Charles Dodgson.