Carbon has two stable isotopes: carbon-12 (12C), and carbon-13 (13C). In addition, there are tiny amounts of the unstable isotope carbon-14 (14C) on earth. 14C has a half life of just under 6000 years, and so would have long ago vanished from the earth, were it not for its constant formation by cosmic ray impacts on nitrogen in the atmosphere. When cosmic rays enter the atmosphere they undergo various transformations, including the production of neutrons. The resulting neutrons participate in the following reacion:
This reaction is relatively common, as nitrogen constitutes nearly 80% of Earth's atmosphere. The highest rate of carbon-14 production takes place at altitudes of 30,000-50,000 feet, and at higher geomagnetic lattitudes, but the carbon-14 spreads evenly throughout the atmosphere and reacts with oxygen to form carbon dioxide. Carbon dioxide also permeates the oceans, dissolving in the water. Since it is assumed that the cosmic ray flux is constant over long periods of time, carbon-14 is assumed to be continuously produced at a constant rate and therefore that the proportion of radioactive to nonradioactive carbon throughout the Earth's atmosphere and oceans is constant.
Plants take up atmospheric carbon dioxide by photosynthesis, and are eaten by animals, so every living thing is constantly exchanging 14C with its environment as long as it lives. Once it dies, however, this exchange stops, and the amount of 14C gradually decreases through radiocative decays. This decay can be used to get a measure of how long ago a piece of once-living material died.
Measurements were originally made by counting the radioactive decay of individual carbon atoms, but this was relatively insensitive and subject to statistical errors: there is never much 14C to begin with, and a half-life that long means that very few of the atoms will decay while you're trying to detect them. Sensitivity and accuracy have since been greatly increased by the use of mass-spectrometric techniques, where the 14C atoms can be counted directly. Raw radiocarbon measurements are usually reported as years "before present" (BP). This is the number of radiocarbon years before 1950, based on a nominal (and fictitiously constant) level of 14C in the atmosphere equal to the 1950 level.
Radiocarbon labs generally report an uncertainty, e.g., 3000±30BP indicates a standard deviation of 30 radiocarbon years. Traditionally this includes only the statistical counting uncertainty and some labs supply an "error multiplier" that can be multiplied by the uncertainty to account for other sources of error in the measuring process. Additional error is likely to arise from the nature and collection of the sample itself, e.g., a tree may accumulate carbon over a significant period of time and the wood turned into an artifact some time after the death of the tree. It is sometimes stated that burnt material can be reliably dated to the time of burning.
The maximum range of radiocarbon dating appears to be about 50,000 years, after which the amount of 14C is too low to be distiguished from background radiation. The K-Ar and Uranium decay series are used in dating older objects (see Radiometric dating).
The raw BP date can not be used directly as a calendar date, because the assumption that the level of 14C remains constant does not hold true in practice. The level is maintained by high energy particles interacting with the earth's upper atmosphere, which may be affected by changes in the earth's magnetic field or in the cosmic ray background. In addition there are substantial reservoirs of carbon in organic matter and in the ocean and changing climate can sometimes disrupt the carbon flow betweeen these reservoirs and the atmosphere. The level has also been affected by human activities -- it was almost doubled for a short period due to atomic bomb tests in the 1950s and 1960s and has been reduced by the release of large amounts of CO2 from ancient organic sources where 14C is not present -- the fossil fuels used in industry and transportation.
The BP dates are therefore calibrated to give calendar dates. Standard calibration curves are available, based on comparison of radiocarbon dates with other methods such as examination of tree growth rings (dendrochronology), ice and sediment cores and coral samples. The difference between the Julian calendar and the Gregorian calendar can be ignored, because it's insignificant compared to the measurement uncertainty.
The calibration curves can vary significantly from a straight line, so comparison of uncalibrated radiocarbon dates (e.g., plotting them on a graph or subtracting dates to give elapsed time) is likely to give misleading results. There are also significant plateaus in the curves, such as the one at 10000 radiocarbon years BP, which is believed to be associated with changing ocean circulation at the end of the Younger Dryas period. The accuracy of radiocarbon dating is lower for samples originating from such plateau periods.
Carbon dating was developed by a team led by Willard Libby. Originally a Carbon-14 half-life of 5568±30 years was used, which is now known as the Libby half-life. Later a more accurate figure of 5730±40 years was measured, which is known as the Cambridge half-life. However laboratories continue to use the Libby figure to avoid confusion. An uncalibrated dating using the Libby figure could be improved by multiplying by the ratio of these numbers (approximately 1.03), but this is usually unnecessary since the adjustment is included in modern calibration curves.
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