Radiocarbon dating is the use of the naturally occurring isotope of carbon-14 in radiometric dating to determine the age of organic materials, up to ca. 50,000 years. Within archaeology it is considered an absolute dating technique.

Basics

Carbon has two stable isotopes: carbon-12 (¹²C), and carbon-13 (¹³C). In addition, there are tiny amounts of the unstable (radioactive) 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 earth's atmosphere. When cosmic rays enter the atmosphere they undergo various transformations, including the production of neutrons. The resulting neutrons participate in the following reaction:

n + ¹⁴N !’ ¹⁴C + ¹H

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 latitudes, 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 non-radioactive carbon throughout the Earth's atmosphere and oceans is constant: ca. 1 ppt (600 billion atoms/mole). Note that, because of calibration curves, this assumption does not have to hold for ¹⁴C measurements to be an accurate measure of an object's age. If calibration curves are used, the accuracy of these curves will be the limiting factor in age determination.

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 radioactive decay. 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Measurements were originally made by counting the radioactive decay of individual carbon atoms, but this was relatively insensitive and subject to statistical errors: there is never much ¹⁴C to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 their detection is attempted (4 atoms/s/mole just after death, hence e.g. 1 atom/s/mole after 10 000 years).

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 assumed constant - see "calibration" below) 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 distinguished from background radiation. The K-Ar and uranium decay series are used in dating older objects (see Radiometric dating).

Calibration

The raw BP date cannot be used directly as a calendar date, because the assumption that the level of ¹⁴C absorption 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, e.g. variations caused by solar storms. In addition there are substantial reservoirs of carbon in organic matter, the ocean, ocean sediments (see methane hydrate), and sedimentary rocks; and changing climate can sometimes disrupt the carbon flow between 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 (http://www.calpal-online.de) to give calendar dates. Standard calibration curves (http://www.calpal.de/calpal/manual/calibration_curves.htm) are available, based on comparison of radiocarbon dates with other methods such as examination of tree growth rings (dendrochronology), ice cores, deep ocean sediment cores, lake sediment varves, coral samples, and speleothems (cave deposits).

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 from 11000 to 10000 radiocarbon years BP, which is believed to be associated with changing ocean circulation during the Younger Dryas period. The accuracy of radiocarbon dating is lower for samples originating from such plateau periods.

It has been noted that the plateau itself can be used as a time marker when it appears in a time series.

Libby vs Cambridge half-life

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.

Examples of Carbon Dating and Historical Disputes

Shroud of Turin

Santorini

Vinland map

Skeleton Lake

External links

• CalPal - Cologne Radiocarbon Calibration & Paleoclimate Research Package with online manual. (http://www.calpal.de)
• CalPal - Online Radiocarbon Calibration (http://www.calpal-online.de)
• OxCal program for calibration (http://www.rlaha.ox.ac.uk/orau/oxcal.html)
• Layman's explanation of how calibration curves are made (http://www.rlaha.ox.ac.uk/orau/calibration.html)
• Radiocarbon - The main international journal of record for research articles and date lists relevant to 14C (http://www.radiocarbon.org/)
• Further basic information on radiocarbon dating (http://www.informath.org/Basic14C.pdf)