The Earth's atmosphere contains various isotopes of carbon, roughly in constant proportions. These include the main stable isotope (12
C) and an unstable isotope (14
C). Through photosynthesis, plants absorb both forms from carbon dioxide in the atmosphere. When an organism dies, it contains the standard ratio of 14
C to 12
C, but as the 14
C decays with no possibility of replenishment, the proportion of carbon 14 decreases at a known constant rate.
The time taken for it to reduce by half is known as the half-life of 14
C. The measurement of the remaining proportion of 14
C in organic matter thus gives an estimate of its age (a raw radiocarbon age).[4]
However, over time there are small fluctuations in the ratio of 14
C to 12
C in the atmosphere, fluctuations that have been noted in natural records of the past, such as sequences of tree rings and cave deposits.
These C12/C14 ratio records allow fine-tuning, or "calibration", of the raw radiocarbon age, to give a more accurate estimate of the calendar date of the material.
One of the most frequent uses of radiocarbon dating is to estimate the age of organic remains from archaeological sites.
Physical and chemical background[edit]

Carbon has two stable, nonradioactive isotopes: carbon-12 (12
C), and carbon-13 (13
C), and a radioactive isotope, carbon-14 (14
C), also known as radiocarbon.
The half-life of 14
C (the time it takes for half of a given amount of 14
C to decay) is about 5,730 years, so its concentration in the atmosphere might be expected to reduce over thousands of years.

1: Formation of carbon-14
2: Decay of carbon-14
3: The equation is for living organisms, and the inequality is for dead organisms, in which the 14
C then decays (See 2).
However 14
C is constantly being produced in the lower stratosphere and upper troposphere by cosmic rays, which generate neutrons that in turn create 14
C when they strike nitrogen-14 (14
N) atoms.[5]
The carbon dating process is described by the following nuclear reaction, where n represents a neutron and p represents a proton:[6] n + \mathrm{^{14}_{7}N^+} \rightarrow \mathrm{^{14}_{6}C} + p
Once produced, the 14
C quickly combines with the oxygen in the atmosphere to form carbon dioxide (CO
2). Carbon dioxide produced in this way diffuses in the atmosphere, is dissolved in the ocean, and is taken up by plants via photosynthesis. Animals eat the plants, and ultimately the radiocarbon is distributed throughout the biosphere. The combination of the ocean, the atmosphere and the biosphere is referred to as the carbon exchange reservoir.[7]
If it is assumed that the cosmic ray flux has been constant over the last ~100,000 years, then carbon-14 has been produced at a constant rate, and since it is also lost through radioactivity at a constant rate, the proportion of radioactive to non-radioactive carbon is constant. The ratio of 14
C to 12
C in the carbon exchange reservoir is 1.5 parts of 14
C to 1012 parts of 12
C.[7] In addition, about 1% of the reservoir is made up of the stable isotope 13
C.[5]
Invention of the methods[edit]

In the mid-1940s, Willard Libby, then at the University of Chicago, realized that the decay of carbon-14 might lead to a method of dating organic matter. Libby published a paper in 1946 in which he proposed that the carbon in living matter might include carbon-14 as well as non-radioactive carbon.[8][9] Libby and several collaborators proceeded to experiment with methane collected from sewage works in Baltimore, and after isotopically enriching their samples they were able to demonstrate that they contained radioactive carbon-14.
By contrast, methane created from petroleum had no radiocarbon activity. The results were summarized in a paper in Science in 1947, and the authors commented that their results implied it would be possible to date materials containing carbon of organic origin.[8][10] Libby and James Arnold proceeded to experiment with samples of wood