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The technique of radiocarbon dating was discovered by Willard Libby and his colleagues in 1949[2] during his tenure as a professor at the University of Chicago. Libby estimated that the steady state radioactivity concentration of exchangeable carbon-14 would be about 14 disintegrations per minute (dpm) per gram. In 1960, he was awarded the Nobel Prize in chemistry for this work. Willard Frank Libby (December 17, 1908 â€“ September 8, 1980) was an American chemist, famous for his role in the development of radiocarbon dating, a process which revolutionized archaeology. ... The University of Chicago is a private university located principally in the Hyde Park neighborhood of Chicago. ... This is a list of Nobel Prize laureates in Chemistry from 1901 to 2006. ...

One of the frequent uses of the technique is to date organic remains from archaeological sites. Plants fix atmospheric carbon during photosynthesis, so the level of C14 in living plants and animals equals the level of C14 in the atmosphere.

$n + mathrm{~^{14}_{7}N}rightarrowmathrm{~^{14}_{6}C}+ p$
Atmospheric 14C, New Zealand[1] and Austria[2]. The New Zealand curve is representative for the Southern Hemisphere, the Austrian curve is representative for the Northern Hemisphere. Atmospheric nuclear weapon tests almost doubled the concentration of 14C in the Northern Hemisphere [3].

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 is produced at a constant rate and the proportion of radioactive to non-radioactive carbon is constant: ca. 1 part per trillion (600 billion atoms/mole). In 1958 Hessel de Vries showed that the concentration of carbon-14 in the atmosphere varies with time and locality. For the most accurate work, these variations are compensated by means of calibration curves. When these curves are used, their accuracy and shape are the factors that determine the accuracy and age obtained for a given sample. Image File history File links Radiocarbon_bomb_spike. ... Image File history File links Radiocarbon_bomb_spike. ... The cause of Earths magnetic field (the surface magnetic field) is not known for certain, but is possibly explained by dynamo theory. ... General Name, symbol, number oxygen, O, 8 Chemical series nonmetals, chalcogens Group, period, block 16, 2, p Appearance colorless (gas) very pale blue (liquid) Standard atomic weight 15. ... Carbon dioxide is a chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom. ... Animated map exhibiting the worlds oceanic waters. ... Parts per trillion (ppt) is a measure of concentration that is used where very low levels of concentration are significant. ... Hessel de Vries, Dutch physicist at the University of Groningen, furthered the detection methods and applications of radiocarbon dating to a variety of sciences. ... A calibration curve is a graphical display of the functional relationship between the expected value of the observed signal to the analyte amount. ...

Plants take up atmospheric carbon dioxide by photosynthesis, and are ingested 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 beta decay. The leaf is the primary site of photosynthesis in plants. ... In nuclear physics, beta decay (sometimes called neutron decay) is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ...

$mathrm{~^{14}_{6}C}rightarrowmathrm{~^{14}_{7}N}+ e^- + bar{nu}_e$

By emitting an electron and an anti-neutrino, carbon-14 is changed into stable (non-radioactive) nitrogen-14. This decay can be used to measure how long ago 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. Antineutrinos, the antiparticles of neutrinos, are neutral particles produced in nuclear beta decay. ... Nitrogen-14 is a stable, non-radioactive isotope of the nitrogen element. ... In organic chemistry, a carbonate is a salt of carbonic acid. ...

## Computation 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: A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ... A simulation of airflow into a duct using the Navier-Stokes equations A differential equation is a mathematical equation for an unknown function of one or several variables which relates the values of the function itself and of its derivatives of various orders. ...

$frac{dN}{dt} = -lambda N.$

The solution to this equation is:

$N = N_0e^{-lambda t},$,

where, for a given sample of carbonaceous matter:

N0 = number of radiocarbon atoms at t = 0, i.e. the origin of the disintegration time,
N = number of radiocarbon atoms remaining after radioactive decay during the time t,
λ = radiocarbon decay or disintegration constant.
Two related times can be defined:
• mean- or average-life: mean or average time each radiocarbon atom spends in a given sample until it decays.
• half-life: time lapsed for half the number of radiocarbon atoms in a given sample, to decay,

It can be shown that:

$t_{avg} ,$ = $frac{1}{lambda}$ = radiocarbon mean- or average-life = 8033 years (Libby value)
$t_frac{1}{2} ,$ = $t_{avg} cdot ln 2$ = radiocarbon half-life = 5568 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:

$t(BP) = frac{1}{lambda} {ln frac{N}{N_0}}$

and for a raw radiocarbon age:

$t(BP) = -frac{1}{lambda} {ln frac{N}{N_0}}$

After replacing values, the raw radiocarbon age becomes any of the following equivalent formulae:

using logs base e and the average life:

$t(BP) = -t_{avg}cdot ln{frac{N}{N_0}}$

and

using logs base 2 and the half-life:

$t(BP) = -t_frac{1}{2}cdot log_2 frac{N}{N_0}$

## 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 these are 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). Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. ... For other uses, see Atom (disambiguation). ... A proportional counter is a measurement device to count particles of ionizing radiation and measure their energy. ... Liquid scintillation counting is a standard laboratory method in the life-sciences for measuring radiation from beta-emitting nuclides. ... Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ...

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, although the maximum age reported is still around 60,000 years[3]. Mass spectrometry (also known as mass spectroscopy (deprecated)[1] or informally, mass-spec and MS) is an analytical technique used to measure the mass-to-charge ratio of ions. ...

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 old wood, turned into an artifact some time after the death of the tree, will reflect the date of the carbon in the wood. In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. ... The old wood effect or old wood problem is a pitfall encountered in the archaeological technique of Carbon 14 dating. ...

The current maximum radiocarbon age limit lies in the range between 58,000 and 62,000 years (approximately 10 half-lives). This limit is encountered when the radioactivity of the residual 14C in a sample is too low to be distinguished from the background radiation. Background radiation is the ionizing radiation emitted from a variety of natural and artificial radiation sources: sources in the Earth and from those sources that are incorporated in our food and water, which are incorporated in our body, and in building materials and other products that incorporate those radioactive sources...

## Calibration

### The need for calibration

Calibration curve for the radiocarbon dating scale. Data sources: Stuiver et al. (1998)[4]. Samples with a real date more recent than AD 1950 are dated and/or tracked using the N- & S-Hemisphere graphs. See preceding figure.

The atmospheric 14C concentration may differ substantially from the concentration in local water reservoirs. Eroded from CaCO3 or organic deposits, old carbon may be easily assimilated and provide diluted 14C carbon into trophic chains.

### 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). A calibration curve is a graphical display of the functional relationship between the expected value of the observed signal to the analyte amount. ... The growth rings of an unknown tree species, at Bristol Zoo, England Pinus taeda Cross section showing annual rings, Cheraw, South Carolina Pine stump showing growth rings Dendrochronology or tree-ring dating is the method of scientific dating based on the analysis of tree-ring growth patterns. ... Ice Core sample taken from drill. ... This article or section cites very few or no references or sources. ... A varve is an annual layer of sediment or sedimentary rock. ... Extant Subclasses and Orders Alcyonaria    Alcyonacea    Helioporacea Zoantharia    Antipatharia    Corallimorpharia    Scleractinia    Zoanthidea [1][2]  See Anthozoa for details For other uses, see Coral (disambiguation). ... A speleothem (from the Greek for cave deposit) is a formal term for what is also known as a cave formation, or amongst cavers, collectively known as pretties. ...

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. Three temperature records, the GRIP one clearly showing the Younger Dryas event at around 11 kyr BP The Younger Dryas stadial, named after the alpine / tundra wildflower Dryas octopetala, and also referred to as the Big Freeze [1], was a brief (approximately 1300 Â± 70 years [1]) cold climate period following...

### Libby vs Cambridge values

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. Willard Frank Libby (December 17, 1908 â€“ September 8, 1980) was an American chemist, famous for his role in the development of radiocarbon dating, a process which revolutionized archaeology. ...

## Carbon exchange reservoir

Libby's original exchange reservoir hypothesis has recently been criticized by Anatoly Fomenko because of its central assumptions that: (a) the exchange reservoir is constant all over the world; (b) the variations in 14C level are global, such that a small number of samples from a specific year are sufficient for calibration of the dating scale[5]. However, since Libby's early work was published (1950 to 1958), temporal, latitudinal and continental variations in the carbon exchange reservoir have been observed by Hessel de Vries (1958; as reviewed by Lerman et al., 1959, 1960). Subsequently, calibration curves have been developed that allow the correction of raw radiocarbon dates. The reservoir effects that necessitate this correction include: This does not adequately cite its references or sources. ... Hessel de Vries, Dutch physicist at the University of Groningen, furthered the detection methods and applications of radiocarbon dating to a variety of sciences. ...

• Erosion and immersion of carbonate rocks (which are older than 60,000 years and so do not contain 14C) causes an increase in 12C and 13C in the exchange reservoir, which depends on local weather conditions and can vary the ratio of carbon that living organisms incorporate. This is believed negligible since most erosion will flow into the sea[6].
• Volcanic eruptions eject large amount of carbonate into the air, causing an increase in 12C and 13C in the exchange reservoir and can vary the exchange ratio locally. This explains the often irregular dating achieved in volcanic areas[7].
• 14C is known to behave chemically in a way different from 12C and 13C (due to different atomic mass), such that it is possible one isotope will be involved in decomposition reactions out of ratio with other isotopes, but the chemical behavior effects are extremely minor[8].
• The earth is not affected evenly by cosmic radiation, the magnitude of the radiation depends on land altitude and earth's magnetic field strength at any given location, causing minor variation in the local 14C production. This is accounted for by having calibration curves for different locations of the globe. However this could not always be performed, as tree rings for calibration were only recoverable from certain locations in 1958[9].

These effects were first confirmed when samples of wood from around the world, which all had the same age (based on tree ring analysis), showed deviations from the dendrochronological age. Calibration techniques based on tree-ring samples have contributed to increase the accuracy since 1962, when they were accurate to 700 years at worst[10]. The growth rings of an unknown tree species, at Bristol Zoo, England Pinus taeda Cross section showing annual rings, Cheraw, South Carolina Pine stump showing growth rings Dendrochronology or tree-ring dating is the method of scientific dating based on the analysis of tree-ring growth patterns. ...

## Speleothem studies extend 14C calibration

Relatively recent (2001) evidence has allowed scientists to refine the knowledge of one of the underlying assumptions. A peak in the amount of carbon-14 was discovered by scientists studying speleothems in caves in the Bahamas. Stalagmites are calcium carbonate deposits left behind when seepage water, containing dissolved carbon dioxide, evaporates. Carbon-14 levels were found to be twice as high as modern levels[11]. These discoveries improved the calibration for the radiocarbon technique and extended its usefulness to 45,000 years into the past[12]. A speleothem (from the Greek for cave deposit) is a formal term for what is also known as a cave formation, or amongst cavers, collectively known as pretties. ... For other uses, see Cave (disambiguation). ... The Witchs Finger in the Carlsbad Caverns A stalagmite (from the Greek stalagma (Î£Ï„Î±Î»Î±Î³Î¼Î¯Ï„Î·Ï‚), drop or drip) is a type of speleothem that rises from the floor of a limestone cave due to the dripping of mineralized solutions and the deposition of calcium carbonate. ... Calcium carbonate is a chemical compound, with the chemical formula CaCO3. ... Carbon dioxide is a chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom. ...

## Examples

6000 year old human footprints preserved in volcanic mud near lake Managua, Nicaragua. ... HaraldskÃ¦r Woman in glass covered coffin, Velje, Denmark The HaraldskÃ¦r Woman (or Haraldskaer Woman) is a well-preserved Iron Age bog body naturally preserved in a bog in Jutland, Denmark. ... The reconstructed face of the Kennewick Man. ... Roopkund is a place in Uttaranchal India, the location of about three to six hundred skeletons at the edge of a lakeâ€”Skeleton Lake in the Himalayas. ... This article needs additional references or sources for verification. ... Satellite image of Thera The devastating volcanic eruption of Thera in the Bronze Age (dated to ca. ... The Vinland map. ... The Chauvet Cave or Chauvet-Pont-dArc Cave is a cave located near Vallon-Pont-dArc, in the ArdÃ¨che dÃ©partement, in southern France. ...

Earth as seen from Apollo 17 Modern geologists consider the age of the Earth to be around 4. ... Absolute dating is the process of determining a specific archaeological date. ... Cosmogenic isotopes are rare radioactive isotopes created when cosmic radiation interacts with an atomic nucleus. ... The environmental isotopes are a subset of the isotopes, both stable and radioactive, which are the object of Isotope geochemistry. ... Radiometric dating (often called radioactive dating) is a technique used to date materials, based on a comparison between the observed abundance of particular naturally occurring radioactive isotopes and their known decay rates. ... Before the advent of absolute dating in the 20th century, archaeologists and geologists were largely limited to the use of Relative Dating techniques. ... A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...

## References

1. ^ Plastino, W., Kaihola, L., Bartolomei, P., Bella, F. (2001) Cosmic background reduction in the radiocarbon measurement by scintillation spectrometry at the underground laboratory of Gran Sasso, Radiocarbon, 43, 157–161
2. ^ Arnold, J. R. and Libby, W. F. (1949) Age Determinations by Radiocarbon Content: Checks with Samples of Known Age, Science 110, 678–680.
3. ^ "NOSAMS Radiocarbon Data and Calculations", Woods Hole Oceanographic Institution
4. ^ Stuiver, M., Reimer, P. J. and Braziunas, T. F. (1998) High-Precision Radiocarbon Age Calibration for Terrestrial and Marine Samples. Radiocarbon 40, 1127-1151.
5. ^ Libby, W.F. Radiocarbon dating, 2nd Edition, Chicago, University of Chicago Press, 1955.
6. ^ Kolchin, B. A., and Y. A. Shez. Absolute Archaeological Datings and their Problems, Moscow, Nauka, 1972.
7. ^ Kolchin, B. A., and Y. A. Shez. Absolute Archaeological Datings and their Problems, Moscow, Nauka, 1972.
8. ^ Aitken, M. J. Physics and Archaeology, New York, Interscience Publishers, 1961.
9. ^ Crowe, C Carbon-14 activity during the past 5000 years, Nature, Volume 182, 1958.
10. ^ Libby, W.F. Radiocarbon; an Atomic Clock, Annual Science and Humanity journal, 1962.
11. ^ Pennicott, K., Carbon clock could show the wrong time, PhysicsWeb, 10 May 2001
12. ^ Jensen, M. N., Peering deep into the past, The University of Arizona, Department of Physics (2001)
• Bowman, S. (1990) Interpreting the Past: Radiocarbon Dating, University of California Press, ISBN 0-520-07037-2.
• Currie, L. (2004) The Remarkable Metrological History of Radiocarbon Dating II, J. Res. Natl. Inst. Stand. Technol., 109, 185–217.
• de Vries, H. (1958) Kon. Ned. Acad. Wetensch. Proc. Ser. B Phys. Sci. 61, 94; and in Researches in Geochemistry, P. H. Abelson (Ed.) (1959) Wiley, New York, p. 180.
• Friedrich, M., Remmele, S., Kromer, B., Hofmann, J., Spurk, M., Kaiser, K. F., Orcel, C. and Küppers, M. (2004) The 12,460-Year Hohenheim Oak and Pine Tree-Ring Chronology from Central Europe—a Unique Annual Record for Radiocarbon Calibration and Paleoenvironment Reconstructions, Radiocarbon 46, 1111–1122.
• Gove, H. E. (1999) From Hiroshima to the Iceman. The Development and Applications of Accelerator Mass Spectrometry. Bristol: Institute of Physics Publishing.
• Kovar, A. J. (1966) Problems in Radiocarbon Dating at Teotihuacan, American Antiquity 31, 427–430.
• Lerman, J. C., Mook, W. G., Vogel, J. C., and de Waard, H. (1969) Carbon-14 in Patagonian Tree Rings. Science, 165:1123-1125; Lerman, J. C., Mook, W. G., and Vogel, J. C. (1970) Proc. 12th Nobel Symp.
• Lorenz, R. D., Jull, A. J. T., Lunine, J. I. and Swindle, T. (2002) Radiocarbon on Titan, Meteoritics and Planetary Science 37, 867–874.
• Mook, W. G. and van der Plicht, J. (1999) Reporting 14C activities and concentrations, Radiocarbon 41, 227–239.
• Weart, S. (2004) The Discovery of Global Warming - Uses of Radiocarbon Dating.
• Willis, E.H. (1996) Radiocarbon dating in Cambridge: some personal recollections. A Worm's Eye View of the Early Days.

The Woods Hole Oceanographic Institution (WHOI) is a private, nonprofit research and higher education facility dedicated to the study of all aspects of marine science and engineering and to the education of marine researchers. ...

Results from FactBites:

 Article about "Radiocarbon dating" in the English Wikipedia on 24-Apr-2004 (962 words) Radiocarbon dating is the use of a naturally occurring isotope of carbon in radiometric dating to determine the age of organic materials. 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 accuracy of radiocarbon dating is lower for samples originating from such plateau periods.
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