Radiocarbon dating is a radiometric dating method that uses the naturally occurring radioisotope carbon-14 (¹⁴C) to determine the age of carbonaceous materials up to about 60,000 years. Radiometric dating (often called radioactive dating) is a technique used to date materials usually based on a comparison between the observed abundance of a naturally occurring A radionuclide is an Atom with an unstable nucleus, which is a nucleus characterized by excess energy which is available to be imparted either to a newly-created Carbon-14, 14C, or radiocarbon, is a Radioactive isotope of Carbon discovered on February 27, 1940, by Carbonaceous is the defining attribute of a substance rich in Carbon. ^[1] Raw, i. e. uncalibrated, radiocarbon ages are usually reported in radiocarbon years "Before Present" (BP), "Present" being defined as AD 1950. Before Present (BP years are a time scale used in Archaeology, Geology, and other scientific disciplines to specify when events in the past occurred Such raw ages can be calibrated to give calendar dates.

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. Willard Frank Libby ( December 17, 1908 &ndash September 8, 1980) was an American physical chemist, famous for his The University of Chicago is a Private university located principally in the Hyde Park neighborhood 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. The Nobel Prize in Chemistry (Nobelpriset i kemi is awarded annually by the Royal Swedish Academy of Sciences to scientists in the various fields of Chemistry. He first demonstrated the accuracy of radiocarbon dating by accurately measuring the age of wood from an ancient Egyptian royal barge whose age was known from historical documents. Ancient Egypt was an Ancient Civilization in eastern North Africa, concentrated along the lower reaches of the Nile River in what is now

One of the frequent uses of the technique is to date organic remains from archaeological sites. Plants fix atmospheric carbon during photosynthesis, such that the level of ¹⁴C in living plants (and the animals that consume them) approximately equals the level of ¹⁴C in the atmosphere. A difference due to isotope fractionation is corrected after laboratory analyses.

Basic physics

Atmospheric ¹⁴C, New Zealand^[3] and Austria^[4]. New Zealand is an Island country in the south-western Pacific Ocean comprising two main landmasses (the North Island and the South Island Austria (Österreich ( officially the Republic of Austria (Republik Österreich 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^[5].

Carbon has two stable, nonradioactive isotopes: carbon-12 (¹²C), and carbon-13 (¹³C). Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides Carbon-12 is the most abundant of the two stable Isotopes of the element Carbon, accounting for 98 Carbon-13 ( 13C) is a natural stable Isotope of Carbon and one of the Environmental isotopes. In addition, there are trace amounts of the unstable isotope carbon-14 (¹⁴C) on Earth. Carbon-14, 14C, or radiocarbon, is a Radioactive isotope of Carbon discovered on February 27, 1940, by EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 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 create more of the isotope. Half-Life (computer-game page here It's already listed in the disambiguation page For the 1962 Bruce Conner film see Cosmic Ray (film Cosmic rays are energetic particles originating from space that impinge on Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five The neutrons resulting from the cosmic ray interactions participate in the following nuclear reaction on the atoms of nitrogen molecules (N₂) in the atmospheric air:

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. This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. In Nuclear physics, a nuclear reaction is the process in which two nuclei or nuclear particles collide to produce products different from the initial particles Earth 's magnetic field (and the surface magnetic field) is approximately a Magnetic dipole, with one pole near the North pole (see Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single Carbon dioxide also permeates the oceans, dissolving in the water. An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere. 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). "Parts-per" notation is used especially in Science and Engineering, to denote Ratios (relative proportions in measured quantities particularly In 1958 Hessel de Vries showed that the concentration of carbon-14 in the atmosphere varies with time and locality. Hessel de Vries ( Nov 15 1916, Annen - Dec 23 1959, Groningen) was a Dutch physicist at the University of Groningen For the most accurate work, these variations are compensated by means of calibration curves. In Analytical chemistry, a calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard When these curves are used, their accuracy and shape are the factors that determine the accuracy and age obtained for a given sample.

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. Photosynthesis is a Metabolic pathway that converts Light Energy into Chemical energy. Once it dies, however, this exchange stops, and the amount of carbon-14 gradually decreases through radioactive beta decay. In Nuclear physics, beta decay is a type of Radioactive decay in which a Beta particle (an Electron or a Positron) is emitted

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 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:

The solution to this equation is:

,

where, for a given sample of carbonaceous matter:

N₀ = number of radiocarbon atoms at t = 0, i. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the 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:

= = radiocarbon mean- or average-life = 8033 years (Libby value)

= = 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:

For a raw radiocarbon date:

and for a raw radiocarbon age:

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

using logs base e and the average life:

and

using logs base 2 and the half-life:

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. Radioactive decay is the process in which an unstable Atomic nucleus loses energy by emitting ionizing particles and Radiation. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny 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. For samples of sufficient size (several grams of carbon) this method is still widely used in the 2000s. Among others, all the tree ring samples used for the calibration curves (see below) were determined by these counting techniques. Such decay counting, however, is relatively insensitive and subject to large statistical uncertainties for small samples. When there is little carbon-14 to begin with, the long radiocarbon half-life means that very few of the carbon-14 atoms will decay during the time allotted for their detection, resulting in few disintegrations per minute. Half-Life (computer-game page here It's already listed in the disambiguation page

The sensitivity of the method has been greatly increased by the use of Accelerator Mass Spectrometry (AMS). Accelerator mass spectrometry (AMS differs from other forms of Mass spectrometry in that it accelerates ions to extraordinarily high kinetic energies before mass With this technique ¹⁴C atoms can be detected and counted directly vs only detecting those atoms that decay during the time interval allotted for an analysis. AMS allows dating samples containing only a few milligrams of carbon.

Raw radiocarbon ages (i. e. , those not calibrated) are usually reported in "years Before Present" (BP). Before Present (BP years are a time scale used in Archaeology, Geology, and other scientific disciplines to specify when events in the past occurred 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. Year 1950 ( MCML) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar. Radiocarbon dating is a Radiometric dating method that uses the naturally occurring Radioisotope Carbon-14 (14C to determine the age of These raw dates are also based on a slightly-off historic value for the radiocarbon half-life. Such value is used for consistency with earlier published dates (see "Radiocarbon half-tfe" below). Radiocarbon dating is a Radiometric dating method that uses the naturally occurring Radioisotope Carbon-14 (14C to determine the age of See the section on computation for the basis of the calculations.

Radiocarbon dating laboratories generally report an uncertainty for each date. For example, 3000±30BP indicates a standard deviation of 30 radiocarbon years. In Probability and Statistics, the standard deviation is a measure of the dispersion of a collection of values Traditionally this included only the statistical counting uncertainty. However, some laboratories supplied an "error multiplier" that could be multiplied by the uncertainty to account for other sources of error in the measuring process. More recently, the laboratories try to quote the overall uncertainty, which is determined from control samples of known age and verified by international intercomparison exercises ^[6]. In 2008, a typical uncertainty better than ±40 radiocarbon years can be expected for samples younger than 10,000 years. This, however, is only a small part of the uncertaintainty of the final age determination (see section Calibration below). Radiocarbon dating is a Radiometric dating method that uses the naturally occurring Radioisotope Carbon-14 (14C to determine the age of

As of 2007, the limiting age for a 1 milligram sample of graphite is about ten half-lives, approximately 60,000 years^[7]. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. This age is derived from that of the calibration blanks used in an analysis, whose ¹⁴C content is the result of contamination during processing (as a result of this, some facilities^[7] will not report an age greater than 60,000 years for any sample). Calibration is the process of establishing the relationship between a measuring device and the units of measure

A variety of sample processing and instrument-based constraints have been postulated to explain the upper age-limit. To examine instrument-based background activities in the AMS instrument of the W. M. Keck Carbon Cycle Accelerator Mass Spectrometry Laboratory of the University of California, a set of natural diamonds were dated. Natural diamond samples from different sources within rock formations with standard geological ages in excess of 100 my yielded ¹⁴C apparent ages 64,920±430 BP to 80,000±1100 BP as reported in 2007^[8].

Calibration

The need for calibration

Calibration curve for the radiocarbon dating scale. Data sources: Stuiver et al. (1998)^[9]. Samples with a real date more recent than AD 1950 are dated and/or tracked using the N- & S-Hemisphere graphs. See preceding figure.

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 in the earth's magnetosphere. For the 1962 Bruce Conner film see Cosmic Ray (film Cosmic rays are energetic particles originating from space that impinge on In addition there are substantial reservoirs of carbon in organic matter, the ocean, ocean sediments (see methane hydrate), and sedimentary rocks. Methane clathrate, also called methane hydrate or methane ice, is a solid form of water that contains a large amount of Methane within its Crystal Sedimentary rock is one of the three main rock types (the others being igneous and Metamorphic rock) Changing climate can sometimes disrupt the carbon flow between these reservoirs and the atmosphere. Climate encompasses the temperatures humidity rainfall atmospheric particle count and numerous other meteorogical factors in a given region over long periods of 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 lowered by the admixture of large amounts of CO₂ from ancient organic sources relatively depleted in ¹⁴C —the combustion products of fossil fuels used in industry and transportation, known as the Suess effect. A nuclear weapon is an explosive device that derives its destructive force from Nuclear reactions either fission or a combination of fission and fusion. The 1950s Decade refers to the years of 1950 to 1959 inclusive The 1960s decade refers to the years from the beginning of 1960 to the end of 1969 Fossil fuels or mineral fuels are fossil source Fuels that is Hydrocarbons found within the top layer of the Earth’s crust. The Suess effect is dilution of the atmospheric concentrations of heavy isotopes of carbon (13C and 14C by the admixture of large amounts of fossil-fuel

Calibration methods

The raw radiocarbon dates, in BP years, are calibrated to give calendar dates. Standard calibration curves are available, based on comparison of radiocarbon dates of samples that can be dated independently by other methods such as examination of tree growth rings (dendrochronology), deep ocean sediment cores, lake sediment varves, coral samples, and speleothems (cave deposits). In Analytical chemistry, a calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard Dendrochronology (from Greek grc δένδρον dendron, "tree" grc χρόνος khronos, "time" and grc -λογία Sediment is any particulate matter that can be transported by fluid flow and which eventually is deposited as a layer of solid particles on the bed or bottom of a body of A varve is an annual layer of Sediment or Sedimentary rock. The word 'varve' is derived from the Swedish word varv whose Corals are Marine organisms from the class Anthozoa and exist as small Sea anemone –like Polyps typically in colonies of many A speleothem (from the Greek for "cave deposit" commonly known as a cave formation, is a secondary mineral deposit formed in a Cave.

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 Younger Dryas Stadial, named after the alpine / tundra wildflower Dryas octopetala, and also referred to as the Big Freeze, was a brief (approximately Over the historical period from 0 to 10,000 years BP, the average width of the uncertainty of calibrated dates was found to be 335 years, although in well-behaved regions of the calibration curve the width decreased to about 113 years while in ill-behaved regions it increased to a maximum of 801 years. Significantly, in the ill-behaved regions of the calibration curve, increasing the precision of the measurements does not have a significant effect on increasing the accuracy of the dates. ^[10]

The 2004 version of the calibration curve extends back quite accurately to 26,000 years BP. Any errors in the calibration curve do not contribute more than ±16 years to the measurement error during the historic and late prehistoric periods (0 - 6,000 yrs BP) and no more than ±163 years over the entire 26,000 years of the curve, although its shape can reduce the accuracy as mentioned above. ^[11]

Radiocarbon half-life

Libby vs Cambridge values

Carbon dating was developed by a team led by Willard Libby. Willard Frank Libby ( December 17, 1908 &ndash September 8, 1980) was an American physical chemist, famous for his 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. This is, however, not relevant for radiocarbon dating. If calibration is applied, the half-life cancels out, as long as the same value is used throughout the calculations. Laboratories continue to use the Libby figure to avoid inconsistencies with previous publications.

Carbon exchange reservoir

Libby's original exchange reservoir hypothesis assumes that the exchange reservoir is constant all over the world. The calibration method also assumes that the temporal variation in ¹⁴C level is global, such that a small number of samples from a specific year are sufficient for calibration. ^[12] However, since Libby's early work was published (1950 to 1958), latitudinal and continental variations in the carbon exchange reservoir have been observed by Hessel de Vries (1958; as reviewed by Lerman et al. Hessel de Vries ( Nov 15 1916, Annen - Dec 23 1959, Groningen) was a Dutch physicist at the University of Groningen , 1959, 1960). Subsequently, methods have been developed that allow the correction of these so-called reservoir effects, including:

• When CO₂ is transferred from the atmosphere to the oceans, it initially shares the ¹⁴C concentration of the atmosphere. However, turnaround times of CO₂ in the ocean are similar to the half-life of ¹⁴C (making ¹⁴C also a dating tool for ocean water, ^[13]). Marine organisms feed on this "old" carbon, and thus their radiocarbon age reflects the time of CO₂ uptake by the ocean rather than the dead of the organism. This marine reservoir effect is partly handled by a special marine calibration curve ^[14], but local deviation of several 100 years exist.

• Erosion and immersion of carbonate rocks (which are generally older than 80,000 years and so wouldn't contain measurable 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 for the atmosphere and atmosphere-derived carbon since most erosion will flow into the sea. ^[15]. The atmospheric ¹⁴C concentration may differ substantially from the concentration in local water reservoirs. Eroded from CaCO₃ or organic deposits, old carbon may be assimilated easily and provide diluted ¹⁴C carbon into trophic chains. So the method is less reliable for such materials as well as for samples derived from animals with such plants in their food chain.

• 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. ^[15]

• 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. ^[16]

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. Dendrochronology (from Greek grc δένδρον dendron, "tree" grc χρόνος khronos, "time" and grc -λογία Calibration techniques based on tree-ring samples have contributed to increase the accuracy since 1962, when they were accurate to 700 years at worst. ^[17]

Fomenko's recent analyses and criticism of the radiocarbon dating method are, thus, invalid because they refer to the earlier, now obsolete, radiocarbon dates. Fomenko is a Russian and Ukrainian surname and may refer to Anatoly Fomenko, Russian mathematician Mykhailo Fomenko, Ukrainian football

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. A speleothem (from the Greek for "cave deposit" commonly known as a cave formation, is a secondary mineral deposit formed in a Cave. A cave is a natural underground void large enough for a human to enter The Bahamas, officially the Commonwealth of The Bahamas, is an independent sovereign English -speaking country consisting of two thousand Cays and Stalagmites are calcium carbonate deposits left behind when seepage water, containing dissolved carbon dioxide, evaporates. A stalagmite (from the Greek stalagma ("Σταλαγμίτης" "drop" or "drip" is a Calcium carbonate is a Chemical compound with the Chemical formula Ca[[Carbon C]] O 3 Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single Carbon-14 levels were found to be twice as high as modern levels^[18]. These discoveries improved the calibration for the radiocarbon technique and extended its usefulness to 45,000 years into the past^[19].

Examples

• Ancient footprints of Acahualinca
• Chauvet Cave
• Dolaucothi
• Haraldskær Woman
• Kennewick Man
• Skeleton Lake
• Shroud of Turin
• Thera eruption
• Vinland map

See also

• Age of the Earth
• Cosmogenic isotopes
• Environmental isotopes
• Discussion of half-life and average-life or mean-lifetime

Notes

References

• Bowman, Sheridan (1990). Interpreting the Past: Radiocarbon Dating. Berkeley: University of California Press. ISBN 0520070372.  
• Currie, L. (2004). "The Remarkable Metrological History of Radiocarbon Dating II". J. Res. Natl. Inst. Stand. Technol. 109: 185–217.  
• de Vries, H. L. (1958). "Variation in Concentration of Radiocarbon with Time and Location on Earth", Proceedings Koninlijke Nederlandse Akademie Wetenschappen B, 61: 94-102; and in Researches in Geochemistry, P. H. Abelson (Ed. ) (1959) Wiley, New York, p. 180.
• Friedrich, M. ; et al. (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, Anton J. (1966). "Problems in Radiocarbon Dating at Teotihuacan". American Antiquity 31: 427–430. doi:10.2307/2694748. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  
• Lerman, J. C. ; Mook, W. G. ; Vogel, J. C. ; de Waard, H. (1969). "Carbon-14 in Patagonian Tree Rings". Science 165 (3898): 1123–1125. doi:10.1126/science.165.3898.1123. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  ; 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. ; Swindle, T. (2002). "Radiocarbon on Titan". Meteoritics and Planetary Science 37: 867–874.  
• Mook, W. G. ; 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.

External links

• Radiocarbon - The main international journal of record for research articles and date lists relevant to 14C
• C14dating.com - General information on Radiocarbon dating
• NOSAMS: National Ocean Sciences Accelerator Mass Spectrometry Facility at the Woods Hole Oceanographic Institution
• Discussion of calibration
• Several calibration programs can be found at www.radiocarbon.org
• CalPal Online (Cologne Radiocarbon Calibration & Paleoclimate Research Package)
• OxCal program (Oxford Calibration)
• Fairbanks' Radiocarbon Calibration program (for prior to 12400 BP)
• Further basic information on radiocarbon dating from UC Santa Barbara