Radiocarbon dating

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Radiocarbon dating is a radiometric dating method that uses the naturally occurring isotope carbon-14 to determine the age of carbonaceous materials up to ca 60,000 years. Within archaeology it is considered an absolute dating technique. The technique was discovered by Willard Frank Libby and his colleagues in 1949. In 1960, Libby was awarded the Nobel Prize in chemistry for radiocarbon dating.

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Basic chemistry

Carbon has two stable, nonradioactive isotopes: carbon-12 (12C), and carbon-13 (13C). In addition, there are tiny amounts of the unstable isotope carbon-14 (14C) on Earth. Carbon-14 has a half-life of 5730 years and would have long ago vanished from Earth were it not for the unremitting cosmic ray impacts on nitrogen in the Earth's atmosphere, which forms more of the isotope. When cosmic rays enter the atmosphere, they undergo various transformations, including the production of neutrons. The resulting neutrons participate in the following reaction on one of the N atoms being knocked out of a Nitrogen (N2) molecule in the atmosphere:

1n + 14N → 14C + 1p

Image:Radiocarbon bomb spike.svg

The highest rate of carbon-14 production takes place at altitudes of 9 to 15 km (30,000 to 50,000 ft), and at high 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. For approximate analysis it is assumed that the cosmic ray flux is constant over long periods of time; thus carbon-14 could be 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 surface oceans is constant: ca. 1 parts per trillion (600 billion atoms/mole). For more accurate work, the temporal variation of the cosmic ray flux can be compensated for with calibration curves. If these curves are used, their accuracy and shape will be the limiting factors in the determination of the radiocarbon age range of a given sample.

Plants take up atmospheric carbon dioxide by photosynthesis, and are eaten by animals, so every living thing is constantly exchanging carbon-14 with its environment as long as it lives. Once it dies, however, this exchange stops, and the amount of carbon-14 gradually decreases through radioactive decay.

14C → 14N + 0β

By emitting a β particle(Beta decay), carbon-14 is changed into stable (non-radioactive) nitrogen-14. This decay can be used to get a measure of how long ago a piece of once-living material died. However, aquatic plants obtain some of their carbon from dissolved carbonates which are likely to be very old, and thus deficient in the carbon-14 isotope, so the method is less reliable for such materials as well as for samples derived from animals with such plants in their food-chain.

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Measurements and scales

Measurements are traditionally made by counting the radioactive decay of individual carbon atoms by gas proportional counting or by liquid scintillation counting, but this is relatively insensitive and subject to relatively large statistical uncertainties for small samples (below about 1g carbon). If there is little carbon-14 to begin with, a half-life that long means that very few of the atoms will decay while their detection is attempted (4 atoms/s) /mol just after death, hence e.g. 1 (atom/s)/mol after 10,000 years). Sensitivity has since been greatly increased by the use of accelerator-based mass-spectrometric (AMS) techniques, where all the 14C atoms can be counted directly, rather than only those decaying during the counting interval allotted for each analysis. The AMS technique allows one to date samples containing only a few milligrams of carbon.

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 carbon-14 in the atmosphere equal to the 1950 level. They are also based on a slightly off historic value for the half-life maintained for consistency with older publications (see "Libby vs Cambridge half-life" below). See the note, below, for the basis of the computations. Corrections for isotopic fractionation have not been included in the present note.

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. Such wood, turned into an artifact some time after the death of the tree, will reflect the date of the carbon in the wood.

The current maximum radiocarbon age limit lies in the range between 58,000 and 62,000 years. This limit is encountered when the radioactivity of the residual 14C in a sample is too low to be distinguished from the background radiation.

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Calibration

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The need for calibration

Image:Radiocarbon dating calibration.svg A raw BP date cannot be used directly as a calendar date, because the level of atmospheric 14C has not been strictly constant during the span of time that can be radiocarbon dated. The level is affected by variations in the cosmic ray intensity which is affected by 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. 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, known as the Suess effect.

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Calibration methods

The raw radiocarbon dates, in BP years, are therefore calibrated to give calendar dates. Standard calibration curves are available, based on comparison of radiocarbon dates of samples that can be independently dated by 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 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 11,000 to 10,000 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.


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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 determined, which is known as the Cambridge half-life. However laboratories continue to use the Libby figure to avoid inconsistencies when comparing raw dates and when using calibration curves to obtain calendrical dates.

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See also

Articles on

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Examples of carbon dating

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References

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External links

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Note: Computations of ages and dates

The radioactive decay of carbon-14 follows an exponential decay. A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. Symbolically, this can be expressed as the following differential equation, where N is the quantity and λ is a positive number called the decay constant:

<math>\frac{dN}{dt} = -\lambda N.</math>

The solution to this equation is:

<math>N = Ce^{-\lambda t} \,</math>,

where <math>C</math> is the initial value of <math>N</math>.

For the particular case of radiocarbon decay, this equation is written:

<math>N = N_0e^{-\lambda t}\,</math>,

where, for a given sample of carbonaceous matter:

<math>N_0</math> = number of radiocarbon atoms at <math>t = 0</math>, i.e. the origin of the disintegration time,
<math>N</math> = number of radiocarbon atoms remaining after radioactive decay during the time <math>t</math>,
<math>{\lambda} = </math>radiocarbon decay or disintegration constant.
Two related times can be defined:
  • half-life: time lapsed for half the number of radiocarbon atoms in a given sample, to decay,
  • mean- or average-life: mean or average time each radiocarbon atom spends in a given sample until it decays.

It can be shown that:

<math>t_{1/2}</math> = <math> \frac{\ln 2}{\lambda} </math> = radiocarbon half-life = 5568 years (Libby value)
<math>t_{avg}</math> = <math> \frac{1}{\lambda} </math> = radiocarbon mean- or average-life = 8033 years (Libby value)

Notice that dates are customarily given in years BP which implies t(BP) = -t because the time arrow for dates runs in reverse direction from the time arrow for the corresponding ages. From these considerations and the above equation, it results:

For a raw radiocarbon date:

<math>t(BP) = \frac{1}{\lambda} {\ln \frac{N}{N_0}}</math>

and for a raw radiocarbon age:

<math>t = -\frac{1}{\lambda} {\ln \frac{N}{N_0}}</math>Template:Link FA

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