TheInfoList

Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing
organic material Organic matter, organic material, or natural organic matter refers to the large source of carbon-based compounds found within natural and engineered, terrestrial and aquatic environments. It is matter In classical physics and general chem ...
by using the properties of

, a
radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...

isotope of carbon. The method was developed in the late 1940s at the
University of Chicago The University of Chicago (UChicago) is a in . Founded in 1890, its main campus is located in Chicago's neighborhood. In Fall 2021, it enrolled 18,452 students, including 7,559 undergraduates and 10,893 graduate students. The university is ...
by
Willard Libby Willard Frank Libby (December 17, 1908 – September 8, 1980) was an American physical chemist noted for his role in the 1949 development of radiocarbon dating Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a me ...
. It is based on the fact that radiocarbon () is constantly being created in the Earth's atmosphere by the interaction of
cosmic ray Cosmic rays are high-energy proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approx ...
s with atmospheric
nitrogen Nitrogen is the chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same ...

. The resulting combines with atmospheric
oxygen Oxygen is the chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same ...

carbon dioxide Carbon dioxide (chemical formula A chemical formula is a way of presenting information about the chemical proportions of atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is ...

, which is incorporated into plants by
photosynthesis Photosynthesis is a process used by plants and other organisms to into that, through , can later be released to fuel the organism's activities. Some of this chemical energy is stored in molecules, such as s and es, which are synthesized fro ...

; animals then acquire by eating the plants. When the animal or plant dies, it stops exchanging carbon with its environment, and thereafter the amount of it contains begins to decrease as the undergoes
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ...

. Measuring the amount of in a sample from a dead plant or animal, such as a piece of wood or a fragment of bone, provides information that can be used to calculate when the animal or plant died. The older a sample is, the less there is to be detected, and because the
half-life Half-life (symbol ''t''1⁄2) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents an ...
of (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to approximately 50,000 years ago, although special preparation methods occasionally make accurate analysis of older samples possible. Libby received the
Nobel Prize in Chemistry ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "MD ...
for his work in 1960. Research has been ongoing since the 1960s to determine what the proportion of in the atmosphere has been over the past fifty thousand years. The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age. Other corrections must be made to account for the proportion of in different types of organisms (fractionation), and the varying levels of throughout the
biosphere The biosphere (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 ...
(reservoir effects). Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the 1950s and 1960s. Because the time it takes to convert biological materials to
fossil fuels A fossil fuel is a hydrocarbon In organic chemistry, a hydrocarbon is an organic compound , CH4; is among the simplest organic compounds. In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen che ...
is substantially longer than the time it takes for its to decay below detectable levels, fossil fuels contain almost no . As a result, beginning in the late 19th century, there was a noticeable drop in the proportion of as the carbon dioxide generated from burning fossil fuels began to accumulate in the atmosphere. Conversely,
nuclear testing Nuclear weapons tests are experiments carried out to determine the effectiveness, yield, and explosive capability of nuclear weapons. Testing nuclear weapons offers practical information about how the weapons function, as well as how detonations ...
increased the amount of in the atmosphere, which reached a maximum in about 1965 of almost double the amount present in the atmosphere prior to nuclear testing. Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of
beta radiation A beta particle, also called beta ray or beta radiation (symbol β), is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, β− ...
emitted by decaying atoms in a sample. More recently,
accelerator mass spectrometry Accelerator mass spectrometry (AMS) is a form of mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are typically presented as a mass spectrum, a plot of intens ...
has become the method of choice; it counts all the atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples (as small as individual plant seeds), and gives results much more quickly. The development of radiocarbon dating has had a profound impact on
archaeology Archaeology or archeology is the study of human activity through the recovery and analysis of material culture. Archaeology is often considered a branch of socio-cultural anthropology, but archaeologists also draw from biological, geological ...
. In addition to permitting more accurate dating within archaeological sites than previous methods, it allows comparison of dates of events across great distances. Histories of archaeology often refer to its impact as the "radiocarbon revolution". Radiocarbon dating has allowed key transitions in prehistory to be dated, such as the end of the last ice age, and the beginning of the
Neolithic The Neolithic period is the final division of the Stone Age, with a wide-ranging set of developments that appear to have arisen independently in several parts of the world. It is first seen about 12,000 years ago when the first developments of ...
and
Bronze Age The Bronze Age is a prehistoric that was characterized by the use of , in some areas , and other early features of urban . The Bronze Age is the second principal period of the , as proposed in modern times by , for classifying and studying a ...
in different regions.

# Background

## History

In 1939,
Martin Kamen Martin David Kamen (August 27, 1913, Toronto Toronto is the capital city of the Provinces and territories of Canada, Canadian province of Ontario. With a recorded population of 2,731,571 in 2016, it is the List of the 100 largest municipal ...
and
Samuel Ruben Samuel Ruben (14 July 1900 – 16 July 1988) was an American inventor who made lasting contributions to electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential, as a measu ...
of the Radiation Laboratory at Berkeley began experiments to determine if any of the elements common in organic matter had isotopes with half-lives long enough to be of value in biomedical research. They synthesized using the laboratory's cyclotron accelerator and soon discovered that the atom's
half-life Half-life (symbol ''t''1⁄2) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents an ...
was far longer than had been previously thought.Taylor & Bar-Yosef (2014), p. 268. This was followed by a prediction by Serge A. Korff, then employed at the
Franklin Institute The Franklin Institute is a science museum and the center of science education and research in Philadelphia, Pennsylvania. It is named after the American scientist and wikt:statesman, statesman Benjamin Franklin, and houses the Benjamin Franklin ...
in
Philadelphia Philadelphia (colloquially known simply as Philly) is the largest city in the of in the . It is the in the United States and the city in the state of Pennsylvania, with a 2020 population of 1,603,797. It is also the in the Northeastern U ...

, that the interaction of
thermal neutrons The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as th ...
with in the upper atmosphere would create .Taylor & Bar-Yosef (2014), p. 269. It had previously been thought that would be more likely to be created by
deuteron Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes The term stable isotope has a meaning similar to stable nuclide, but is preferably used when speaking of nuclides of a specific element ...
s interacting with . At some time during World War II,
Willard Libby Willard Frank Libby (December 17, 1908 – September 8, 1980) was an American physical chemist noted for his role in the 1949 development of radiocarbon dating Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a me ...
, who was then at Berkeley, learned of Korff's research and conceived the idea that it might be possible to use radiocarbon for dating. In 1945, Libby moved to the
University of Chicago The University of Chicago (UChicago) is a in . Founded in 1890, its main campus is located in Chicago's neighborhood. In Fall 2021, it enrolled 18,452 students, including 7,559 undergraduates and 10,893 graduate students. The university is ...
, where he began his work on radiocarbon dating. He published a paper in 1946 in which he proposed that the carbon in living matter might include as well as non-radioactive carbon.Bowman (1995), pp. 9–15. Libby and several collaborators proceeded to experiment with
methane Methane (, ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Earth ...
collected from sewage works in Baltimore, and after isotopically enriching their samples they were able to demonstrate that they contained . By contrast, methane created from petroleum showed no radiocarbon activity because of its age. The results were summarized in a paper in ''
Science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts ( descriptive knowledge), skills (procedural knowledge), or objects ...
'' in 1947, in which the authors commented that their results implied it would be possible to date materials containing carbon of organic origin. Libby and proceeded to test the radiocarbon dating theory by analyzing samples with known ages. For example, two samples taken from the tombs of two Egyptian kings, Zoser and
Sneferu Sneferu ( snfr-wj "He has perfected me", from ''Ḥr-nb-mꜣꜥt-snfr-wj'' "Horus, Lord of Maat, has perfected me", also read Snefru or Snofru), well known under his Hellenized name Soris ( grc-koi, Σῶρις by Manetho), was the founding phar ...
, independently dated to 2625 BC plus or minus 75 years, were dated by radiocarbon measurement to an average of 2800 BC plus or minus 250 years. These results were published in ''Science'' in December 1949.Aitken1990, pp. 60–61. Within 11 years of their announcement, more than 20 radiocarbon dating laboratories had been set up worldwide. In 1960, Libby was awarded the
Nobel Prize in Chemistry ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "MD ...
for this work.

## Physical and chemical details

In nature,
carbon Carbon (from la, carbo "coal") is a with the C and 6. It is lic and —making four s available to form s. It belongs to group 14 of the periodic table. Carbon makes up only about 0.025 percent of Earth's crust. Three occur naturally, ...

exists as three isotopes, two stable, nonradioactive:
carbon-12 Carbon-12 (12C) is the more abundant of the two stable A stable is a building in which livestock Livestock is commonly defined as domesticated Domestication is a sustained multi-generational relationship in which one group of organisms ...

(), and
carbon-13Carbon-13 (13C) is a natural, stable isotope A stable is a building in which livestock, especially horses, are kept. It most commonly means a building that is divided into separate stalls for individual animals and livestock. There are many d ...

carbon-14 Carbon-14 (14C), or radiocarbon, is a radioactive isotope A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry ...

(), also known as "radiocarbon". The half-life of (the time it takes for half of a given amount of to ) is about 5,730 years, so its concentration in the atmosphere might be expected to decrease over thousands of years, but is constantly being produced in the lower
stratosphere File:Stratosphere Temperature Trend.jpg, This image shows the temperature trend in the lower stratosphere as measured by a series of satellite-based instruments between January 1979 and December 2005. The lower stratosphere is centered around 18 k ...

and upper
troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour (99.9839 °C) , - , Boiling point , , - , specific g ...
, primarily by galactic
cosmic ray Cosmic rays are high-energy proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approx ...
s, and to a lesser degree by solar cosmic rays. These cosmic rays generate neutrons as they travel through the atmosphere which can strike
nitrogen-14 Natural nitrogen Nitrogen is the chemical element with the Symbol (chemistry), symbol N and atomic number 7. It was first discovered and isolated by Scottish physician Daniel Rutherford in 1772. Although Carl Wilhelm Scheele and Henry Cavendis ...

() atoms and turn them into . The following
nuclear reaction In nuclear physics Nuclear physics is the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and t ...
is the main pathway by which is created: : n + → + p where n represents a
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...

and p represents a
proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collecti ...

.Bianchi & Canuel (2011), p. 35. Once produced, the quickly combines with the oxygen (O) in the atmosphere to form first carbon monoxide (), and ultimately carbon dioxide (). : + → + O : + OH → + H Carbon dioxide produced in this way diffuses in the atmosphere, is dissolved in the ocean, and is taken up by plants via
photosynthesis Photosynthesis is a process used by plants and other organisms to into that, through , can later be released to fuel the organism's activities. Some of this chemical energy is stored in molecules, such as s and es, which are synthesized fro ...

. Animals eat the plants, and ultimately the radiocarbon is distributed throughout the
biosphere The biosphere (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 ...
. The ratio of to is approximately 1.25 parts of to 1012 parts of .Tsipenyuk (1997), p. 343. In addition, about 1% of the carbon atoms are of the stable isotope . The equation for the radioactive decay of is: : → + + By emitting a beta particle (an
electron The electron is a subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has ma ...

, e) and an
electron antineutrino The electron neutrino () is a subatomic lepton In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowle ...
(), one of the neutrons in the nucleus changes to a proton and the nucleus reverts to the stable (non-radioactive) isotope .

## Principles

During its life, a plant or animal is in equilibrium with its surroundings by exchanging carbon either with the atmosphere or through its diet. It will, therefore, have the same proportion of as the atmosphere, or in the case of marine animals or plants, with the ocean. Once it dies, it ceases to acquire , but the within its biological material at that time will continue to decay, and so the ratio of to in its remains will gradually decrease. Because decays at a known rate, the proportion of radiocarbon can be used to determine how long it has been since a given sample stopped exchanging carbon – the older the sample, the less will be left. The equation governing the decay of a radioactive isotope is: : $N = N_0 \, e^\,$ where ''N''0 is the number of atoms of the isotope in the original sample (at time ''t'' = 0, when the organism from which the sample was taken died), and ''N'' is the number of atoms left after time ''t''. ''λ'' is a constant that depends on the particular isotope; for a given isotope it is equal to the
reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another poly ...

of the mean-life – i.e. the average or expected time a given atom will survive before undergoing radioactive decay. The mean-life, denoted by ''τ'', of is 8,267 years, so the equation above can be rewritten as: : $t = \ln\left(N_0/N\right) \cdot \text$ The sample is assumed to have originally had the same / ratio as the ratio in the atmosphere, and since the size of the sample is known, the total number of atoms in the sample can be calculated, yielding ''N''0, the number of atoms in the original sample. Measurement of ''N'', the number of atoms currently in the sample, allows the calculation of ''t'', the age of the sample, using the equation above. The half-life of a radioactive isotope (usually denoted by t1/2) is a more familiar concept than the mean-life, so although the equations above are expressed in terms of the mean-life, it is more usual to quote the value of 's half-life than its mean-life. The currently accepted value for the half-life of is 5,730 ± 40 years. This means that after 5,730 years, only half of the initial will remain; a quarter will remain after 11,460 years; an eighth after 17,190 years; and so on. The above calculations make several assumptions, such as that the level of in the atmosphere has remained constant over time. In fact, the level of in the atmosphere has varied significantly and as a result, the values provided by the equation above have to be corrected by using data from other sources.Aitken1990, pp. 61–66. This is done by calibration curves (discussed below), which convert a measurement of in a sample into an estimated calendar age. The calculations involve several steps and include an intermediate value called the "radiocarbon age", which is the age in "radiocarbon years" of the sample: an age quoted in radiocarbon years means that no calibration curve has been used − the calculations for radiocarbon years assume that the atmospheric / ratio has not changed over time. Calculating radiocarbon ages also requires the value of the half-life for . In Libby's 1949 paper he used a value of 5720 ± 47 years, based on research by Engelkemeir et al. This was remarkably close to the modern value, but shortly afterwards the accepted value was revised to 5568 ± 30 years, and this value was in use for more than a decade. It was revised again in the early 1960s to 5,730 ± 40 years, which meant that many calculated dates in papers published prior to this were incorrect (the error in the half-life is about 3%). For consistency with these early papers, it was agreed at the 1962 Radiocarbon Conference in Cambridge (UK) to use the "Libby half-life" of 5568 years. Radiocarbon ages are still calculated using this half-life, and are known as "Conventional Radiocarbon Age". Since the calibration curve (IntCal) also reports past atmospheric concentration using this conventional age, any conventional ages calibrated against the IntCal curve will produce a correct calibrated age. When a date is quoted, the reader should be aware that if it is an uncalibrated date (a term used for dates given in radiocarbon years) it may differ substantially from the best estimate of the actual calendar date, both because it uses the wrong value for the half-life of , and because no correction (calibration) has been applied for the historical variation of in the atmosphere over time.Aitken1990, pp. 92–95.Bowman (1995), p. 42.

## Carbon exchange reservoir

Carbon is distributed throughout the atmosphere, the biosphere, and the oceans; these are referred to collectively as the carbon exchange reservoir, and each component is also referred to individually as a carbon exchange reservoir. The different elements of the carbon exchange reservoir vary in how much carbon they store, and in how long it takes for the generated by cosmic rays to fully mix with them. This affects the ratio of to in the different reservoirs, and hence the radiocarbon ages of samples that originated in each reservoir. The atmosphere, which is where is generated, contains about 1.9% of the total carbon in the reservoirs, and the it contains mixes in less than seven years.Warneck (2000), p. 690. The ratio of to in the atmosphere is taken as the baseline for the other reservoirs: if another reservoir has a lower ratio of to , it indicates that the carbon is older and hence that either some of the has decayed, or the reservoir is receiving carbon that is not at the atmospheric baseline. The ocean surface is an example: it contains 2.4% of the carbon in the exchange reservoir, but there is only about 95% as much as would be expected if the ratio were the same as in the atmosphere. The time it takes for carbon from the atmosphere to mix with the surface ocean is only a few years, but the surface waters also receive water from the deep ocean, which has more than 90% of the carbon in the reservoir. Water in the deep ocean takes about 1,000 years to circulate back through surface waters, and so the surface waters contain a combination of older water, with depleted , and water recently at the surface, with in equilibrium with the atmosphere. Creatures living at the ocean surface have the same ratios as the water they live in, and as a result of the reduced / ratio, the radiocarbon age of marine life is typically about 400 years.Bowman (1995), pp. 24–27.Cronin (2010), p. 35. Organisms on land are in closer equilibrium with the atmosphere and have the same / ratio as the atmosphere. These organisms contain about 1.3% of the carbon in the reservoir; sea organisms have a mass of less than 1% of those on land and are not shown in the diagram. Accumulated dead organic matter, of both plants and animals, exceeds the mass of the biosphere by a factor of nearly 3, and since this matter is no longer exchanging carbon with its environment, it has a / ratio lower than that of the biosphere.

# Dating considerations

The variation in the / ratio in different parts of the carbon exchange reservoir means that a straightforward calculation of the age of a sample based on the amount of it contains will often give an incorrect result. There are several other possible sources of error that need to be considered. The errors are of four general types: * variations in the / ratio in the atmosphere, both geographically and over time; * isotopic fractionation; * variations in the / ratio in different parts of the reservoir; * contamination.

## Atmospheric variation

In the early years of using the technique, it was understood that it depended on the atmospheric / ratio having remained the same over the preceding few thousand years. To verify the accuracy of the method, several artefacts that were datable by other techniques were tested; the results of the testing were in reasonable agreement with the true ages of the objects. Over time, however, discrepancies began to appear between the known chronology for the oldest Egyptian dynasties and the radiocarbon dates of Egyptian artefacts. Neither the pre-existing Egyptian chronology nor the new radiocarbon dating method could be assumed to be accurate, but a third possibility was that the / ratio had changed over time. The question was resolved by the study of tree rings:Bowman (1995), pp. 16–20.Suess (1970), p. 303.Taylor & Bar-Yosef (2014), pp. 50–52. comparison of overlapping series of tree rings allowed the construction of a continuous sequence of tree-ring data that spanned 8,000 years. (Since that time the tree-ring data series has been extended to 13,900 years.) In the 1960s,
Hans Suess Hans Eduard Suess (December 16, 1909 – September 20, 1993) was an Austria Austria (, ; german: Österreich ), officially the Republic of Austria (german: Republik Österreich, links=no, ), is a landlocked Eastern Alps, East Alpine c ...
was able to use the tree-ring sequence to show that the dates derived from radiocarbon were consistent with the dates assigned by Egyptologists. This was possible because although annual plants, such as corn, have a / ratio that reflects the atmospheric ratio at the time they were growing, trees only add material to their outermost tree ring in any given year, while the inner tree rings don't get their replenished and instead start losing through decay. Hence each ring preserves a record of the atmospheric / ratio of the year it grew in. Carbon-dating the wood from the tree rings themselves provides the check needed on the atmospheric / ratio: with a sample of known date, and a measurement of the value of ''N'' (the number of atoms of remaining in the sample), the carbon-dating equation allows the calculation of ''N''0 – the number of atoms of in the sample at the time the tree ring was formed – and hence the / ratio in the atmosphere at that time. Equipped with the results of carbon-dating the tree rings, it became possible to construct calibration curves designed to correct the errors caused by the variation over time in the / ratio.Bowman (1995), pp. 43–49. These curves are described in more detail
below Below may refer to: *Earth *Ground (disambiguation) *Soil *Floor *Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Fred Below (1926–1988), American blues drummer *Fritz von Below (1853 ...

. Coal and oil began to be burned in large quantities during the 19th century. Both are sufficiently old that they contain little or no detectable and, as a result, the released substantially diluted the atmospheric / ratio. Dating an object from the early 20th century hence gives an apparent date older than the true date. For the same reason, concentrations in the neighbourhood of large cities are lower than the atmospheric average. This fossil fuel effect (also known as the Suess effect, after Hans Suess, who first reported it in 1955) would only amount to a reduction of 0.2% in activity if the additional carbon from fossil fuels were distributed throughout the carbon exchange reservoir, but because of the long delay in mixing with the deep ocean, the actual effect is a 3% reduction.Aitken1990, pp. 71–72. A much larger effect comes from above-ground nuclear testing, which released large numbers of neutrons into the atmosphere, resulting in the creation of . From about 1950 until 1963, when atmospheric nuclear testing was banned, it is estimated that several tonnes of were created. If all this extra had immediately been spread across the entire carbon exchange reservoir, it would have led to an increase in the / ratio of only a few per cent, but the immediate effect was to almost double the amount of in the atmosphere, with the peak level occurring in 1964 for the northern hemisphere, and in 1966 for the southern hemisphere. The level has since dropped, as this bomb pulse or "bomb carbon" (as it is sometimes called) percolates into the rest of the reservoir.

## Isotopic fractionation

Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. In photosynthetic pathways is absorbed slightly more easily than , which in turn is more easily absorbed than . The differential uptake of the three carbon isotopes leads to / and / ratios in plants that differ from the ratios in the atmosphere. This effect is known as isotopic fractionation.Bowman (1995), pp. 20–23.Maslin & Swann (2006), p. 246. To determine the degree of fractionation that takes place in a given plant, the amounts of both and isotopes are measured, and the resulting / ratio is then compared to a standard ratio known as PDB. The / ratio is used instead of / because the former is much easier to measure, and the latter can be easily derived: the depletion of relative to is proportional to the difference in the atomic masses of the two isotopes, so the depletion for is twice the depletion of . The fractionation of , known as , is calculated as follows: : ‰ where the ‰ sign indicates
parts per thousand In science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of Testability, testable explanations and predictio ...
. Because the PDB standard contains an unusually high proportion of , most measured values are negative. For marine organisms, the details of the photosynthesis reactions are less well understood, and the values for marine photosynthetic organisms are dependent on temperature. At higher temperatures, has poor solubility in water, which means there is less available for the photosynthetic reactions. Under these conditions, fractionation is reduced, and at temperatures above 14 °C the values are correspondingly higher, while at lower temperatures, becomes more soluble and hence more available to marine organisms. The value for animals depends on their diet. An animal that eats food with high values will have a higher than one that eats food with lower values. The animal's own biochemical processes can also impact the results: for example, both bone minerals and bone collagen typically have a higher concentration of than is found in the animal's diet, though for different biochemical reasons. The enrichment of bone also implies that excreted material is depleted in relative to the diet. Since makes up about 1% of the carbon in a sample, the / ratio can be accurately measured by
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the of s. The results are presented as a ', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is used in many different fields and is applied ...
. Typical values of have been found by experiment for many plants, as well as for different parts of animals such as bone
collagen Collagen () is the main structural in the found in the body's various s. As the main component of connective tissue, it is the most abundant protein in mammals, making up from 25% to 35% of the whole-body protein content. Collagen consists of ...

, but when dating a given sample it is better to determine the value for that sample directly than to rely on the published values. The carbon exchange between atmospheric and carbonate at the ocean surface is also subject to fractionation, with in the atmosphere more likely than to dissolve in the ocean. The result is an overall increase in the / ratio in the ocean of 1.5%, relative to the / ratio in the atmosphere. This increase in concentration almost exactly cancels out the decrease caused by the upwelling of water (containing old, and hence -depleted, carbon) from the deep ocean, so that direct measurements of radiation are similar to measurements for the rest of the biosphere. Correcting for isotopic fractionation, as is done for all radiocarbon dates to allow comparison between results from different parts of the biosphere, gives an apparent age of about 400 years for ocean surface water.

## Reservoir effects

Libby's original exchange reservoir hypothesis assumed that the / ratio in the exchange reservoir is constant all over the world,Libby (1965), p. 6. but it has since been discovered that there are several causes of variation in the ratio across the reservoir.

### Marine effect

The in the atmosphere transfers to the ocean by dissolving in the surface water as carbonate and bicarbonate ions; at the same time the carbonate ions in the water are returning to the air as . This exchange process brings from the atmosphere into the surface waters of the ocean, but the thus introduced takes a long time to percolate through the entire volume of the ocean. The deepest parts of the ocean mix very slowly with the surface waters, and the mixing is uneven. The main mechanism that brings deep water to the surface is upwelling, which is more common in regions closer to the equator. Upwelling is also influenced by factors such as the topography of the local ocean bottom and coastlines, the climate, and wind patterns. Overall, the mixing of deep and surface waters takes far longer than the mixing of atmospheric with the surface waters, and as a result water from some deep ocean areas has an apparent radiocarbon age of several thousand years. Upwelling mixes this "old" water with the surface water, giving the surface water an apparent age of about several hundred years (after correcting for fractionation). This effect is not uniform – the average effect is about 400 years, but there are local deviations of several hundred years for areas that are geographically close to each other. These deviations can be accounted for in calibration, and users of software such as CALIB can provide as an input the appropriate correction for the location of their samples. The effect also applies to marine organisms such as shells, and marine mammals such as whales and seals, which have radiocarbon ages that appear to be hundreds of years old.

### Hemisphere effect

The northern and southern hemispheres have
atmospheric circulation Atmospheric circulation is the large-scale movement of Atmosphere of Earth, air and together with ocean circulation is the means by which thermal energy is redistributed on the surface of the Earth. The Earth's atmospheric circulation varies from ...

systems that are sufficiently independent of each other that there is a noticeable time lag in mixing between the two. The atmospheric / ratio is lower in the southern hemisphere, with an apparent additional age of about 40 years for radiocarbon results from the south as compared to the north. This is because the greater surface area of ocean in the southern hemisphere means that there is more carbon exchanged between the ocean and the atmosphere than in the north. Since the surface ocean is depleted in because of the marine effect, is removed from the southern atmosphere more quickly than in the north.Hogg et al. (2013), p. 1898. The effect is strengthened by strong upwelling around Antarctica.

### Other effects

If the carbon in freshwater is partly acquired from aged carbon, such as rocks, then the result will be a reduction in the / ratio in the water. For example, rivers that pass over
limestone Limestone is a common type of carbonate In chemistry, a carbonate is a salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of Salt (chemistry), salts; salt in its nat ...

, which is mostly composed of
calcium carbonate Calcium carbonate is a chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) composed of atoms from more than one chemical element, element held together ...

, will acquire carbonate ions. Similarly, groundwater can contain carbon derived from the rocks through which it has passed. These rocks are usually so old that they no longer contain any measurable , so this carbon lowers the / ratio of the water it enters, which can lead to apparent ages of thousands of years for both the affected water and the plants and freshwater organisms that live in it. This is known as the
hard water Hard water is water Water (chemical formula H2O) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living orga ...
effect because it is often associated with calcium ions, which are characteristic of hard water; other sources of carbon such as
humus In soil science, humus (derived in 1790–1800 from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known ...

can produce similar results, and can also reduce the apparent age if they are of more recent origin than the sample. The effect varies greatly and there is no general offset that can be applied; additional research is usually needed to determine the size of the offset, for example by comparing the radiocarbon age of deposited freshwater shells with associated organic material.
Volcanic eruptions Several types of volcanic eruptions—during which lava of pāhoehoe lava, Hawaii, United States , Iceland in 1984 Lava is molten Rock (geology), rock (magma) that has been expelled from the interior of a terrestrial planet (such as Earth) ...
eject large amounts of carbon into the air. The carbon is of geological origin and has no detectable , so the / ratio in the vicinity of the volcano is depressed relative to surrounding areas. Dormant volcanoes can also emit aged carbon. Plants that photosynthesize this carbon also have lower / ratios: for example, plants in the neighbourhood of the
Furnas Furnas is a civil parish In England, a civil parish is a type of administrative parish used for local government. It is a territorial designation which is the lowest tier of local government below districts and counties, or their combined ...

caldera in the
Azores The Azores ( , also ; pt, Açores ), officially the Autonomous Region of the Azores (), is one of the two autonomous regions of Portugal The two Autonomous Regions of Portugal ( pt, Regiões Autónomas de Portugal) are the Azores (''Região A ...

were found to have apparent ages that ranged from 250 years to 3320 years.

## Contamination

Any addition of carbon to a sample of a different age will cause the measured date to be inaccurate. Contamination with modern carbon causes a sample to appear to be younger than it really is: the effect is greater for older samples. If a sample that is 17,000 years old is contaminated so that 1% of the sample is modern carbon, it will appear to be 600 years younger; for a sample that is 34,000 years old, the same amount of contamination would cause an error of 4,000 years. Contamination with old carbon, with no remaining , causes an error in the other direction independent of age – a sample contaminated with 1% old carbon will appear to be about 80 years older than it truly is, regardless of the date of the sample.

# Samples

Samples for dating need to be converted into a form suitable for measuring the content; this can mean conversion to gaseous, liquid, or solid form, depending on the measurement technique to be used. Before this can be done, the sample must be treated to remove any contamination and any unwanted constituents.Bowman (1995), pp. 27–30. This includes removing visible contaminants, such as rootlets that may have penetrated the sample since its burial. Alkali and acid washes can be used to remove humic acid and carbonate contamination, but care has to be taken to avoid removing the part of the sample that contains the carbon to be tested.Aitken1990, pp. 86–89.

## Material considerations

* It is common to reduce a wood sample to just the cellulose component before testing, but since this can reduce the volume of the sample to 20% of its original size, testing of the whole wood is often performed as well. Charcoal is often tested but is likely to need treatment to remove contaminants. * Unburnt bone can be tested; it is usual to date it using
collagen Collagen () is the main structural in the found in the body's various s. As the main component of connective tissue, it is the most abundant protein in mammals, making up from 25% to 35% of the whole-body protein content. Collagen consists of ...

, the protein fraction that remains after washing away the bone's structural material.
Hydroxyproline (2''S'',4''R'')-4-Hydroxyproline, or L-hydroxyproline ( C5H9 O3 N), is an amino acid Amino acids are organic compounds that contain amino (–NH2) and Carboxylic acid, carboxyl (–COOH) functional groups, along with a Substituent, side chain ...

, one of the constituent amino acids in bone, was once thought to be a reliable indicator as it was not known to occur except in bone, but it has since been detected in groundwater. * For burnt bone, testability depends on the conditions under which the bone was burnt. If the bone was heated under reducing conditions, it (and associated organic matter) may have been carbonized. In this case, the sample is often usable. * Shells from both marine and land organisms consist almost entirely of calcium carbonate, either as
aragonite Aragonite is a carbonate mineral Carbonate minerals are those minerals containing the carbonate ion, CO32−. Carbonate divisions Anhydrous carbonates *Calcite group: trigonal **Calcite CaCO3 **Gaspeite (Ni,Mg,Fe2+)CO3 **Magnesite MgCO3 **Otav ...

or as
calcite Image:Calcite.png, 235px, Crystal structure of calcite Calcite is a Carbonate minerals, carbonate mineral and the most stable Polymorphism (materials science), polymorph of calcium carbonate (CaCO3). The Mohs scale of mineral hardness, based on Scr ...

, or some mixture of the two. Calcium carbonate is very susceptible to dissolving and recrystallizing; the recrystallized material will contain carbon from the sample's environment, which may be of geological origin. If testing recrystallized shell is unavoidable, it is sometimes possible to identify the original shell material from a sequence of tests. It is also possible to test
conchiolin 200px, The shell of ''Stenotrema florida'', a land snail. The periostracum is an organic layer of protein which, in this species, is developed into minute hairs, giving the snail a velvety look and feel Conchiolins (sometimes referred to as conchin ...
, an organic protein found in shell, but it constitutes only 1–2% of shell material. * The three major components of peat are
humic acid Humic substances are organic compound In , organic compounds are generally any s that contain - . Due to carbon's ability to (form chains with other carbon s), millions of organic compounds are known. The study of the properties, reactions, an ...

,
humins Humins are carbon-based macromolecular substances, that can be found in soil chemistry Soil chemistry is the study of the chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Som ...
, and
fulvic acidFulvic acids are a family of organic acids, natural compounds, and components of the humus (which is a fraction of soil organic matterSoil organic matter (SOM) is the organic matter component of soil, consisting of plant and animal detritus at va ...

. Of these, humins give the most reliable date as they are insoluble in alkali and less likely to contain contaminants from the sample's environment. A particular difficulty with dried peat is the removal of rootlets, which are likely to be hard to distinguish from the sample material. * Soil contains organic material, but because of the likelihood of contamination by humic acid of more recent origin, it is very difficult to get satisfactory radiocarbon dates. It is preferable to sieve the soil for fragments of organic origin, and date the fragments with methods that are tolerant of small sample sizes. * Other materials that have been successfully dated include ivory, paper, textiles, individual seeds and grains, straw from within mud bricks, and charred food remains found in pottery.

## Preparation and size

Particularly for older samples, it may be useful to enrich the amount of in the sample before testing. This can be done with a thermal diffusion column. The process takes about a month and requires a sample about ten times as large as would be needed otherwise, but it allows more precise measurement of the / ratio in old material and extends the maximum age that can be reliably reported. Once contamination has been removed, samples must be converted to a form suitable for the measuring technology to be used.Bowman (1995), pp. 31–37. Where gas is required, is widely used.Aitken1990, pp. 76–78. For samples to be used in liquid scintillation counters, the carbon must be in liquid form; the sample is typically converted to
benzene Benzene is an organic Organic may refer to: * Organic, of or relating to an organism, a living entity * Organic, of or relating to an anatomical organ (anatomy), organ Chemistry * Organic matter, matter that has come from a once-living organi ...

. For
accelerator mass spectrometry Accelerator mass spectrometry (AMS) is a form of mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are typically presented as a mass spectrum, a plot of intens ...
, solid graphite targets are the most common, although gaseous can also be used.Trumbore (1996), p. 318. The quantity of material needed for testing depends on the sample type and the technology being used. There are two types of testing technology: detectors that record radioactivity, known as beta counters, and accelerator mass spectrometers. For beta counters, a sample weighing at least is typically required. Accelerator mass spectrometry is much more sensitive, and samples containing as little as 0.5 milligrams of carbon can be used.

# Measurement and results

For decades after Libby performed the first radiocarbon dating experiments, the only way to measure the in a sample was to detect the radioactive decay of individual carbon atoms. In this approach, what is measured is the activity, in number of decay events per unit mass per time period, of the sample. This method is also known as "beta counting", because it is the beta particles emitted by the decaying atoms that are detected. In the late 1970s an alternative approach became available: directly counting the number of and atoms in a given sample, via accelerator mass spectrometry, usually referred to as AMS. AMS counts the / ratio directly, instead of the activity of the sample, but measurements of activity and / ratio can be converted into each other exactly. For some time, beta counting methods were more accurate than AMS, but AMS is now more accurate and has become the method of choice for radiocarbon measurements.Walker (2005), p. 23. In addition to improved accuracy, AMS has two further significant advantages over beta counting: it can perform accurate testing on samples much too small for beta counting, and it is much faster – an accuracy of 1% can be achieved in minutes with AMS, which is far quicker than would be achievable with the older technology.

## Beta counting

Libby's first detector was a
Geiger counter A Geiger counter (also known as a Geiger–Müller counter) is an electronic instrument used for detecting and measuring ionizing radiation Ionizing radiation (or ionising radiation), including nuclear radiation, consists of subatomic particles o ...

of his own design. He converted the carbon in his sample to lamp black (soot) and coated the inner surface of a cylinder with it. This cylinder was inserted into the counter in such a way that the counting wire was inside the sample cylinder, in order that there should be no material between the sample and the wire. Any interposing material would have interfered with the detection of radioactivity, since the beta particles emitted by decaying are so weak that half are stopped by a 0.01 mm thickness of aluminium. Libby's method was soon superseded by gas
proportional counterThe proportional counter is a type of gaseous ionization detector device used to measure particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, obj ...
s, which were less affected by bomb carbon (the additional created by nuclear weapons testing). These counters record bursts of ionization caused by the beta particles emitted by the decaying atoms; the bursts are proportional to the energy of the particle, so other sources of ionization, such as background radiation, can be identified and ignored. The counters are surrounded by lead or steel shielding, to eliminate background radiation and to reduce the incidence of cosmic rays. In addition, anticoincidence detectors are used; these record events outside the counter and any event recorded simultaneously both inside and outside the counter is regarded as an extraneous event and ignored. The other common technology used for measuring activity is liquid scintillation counting, which was invented in 1950, but which had to wait until the early 1960s, when efficient methods of benzene synthesis were developed, to become competitive with gas counting; after 1970 liquid counters became the more common technology choice for newly constructed dating laboratories. The counters work by detecting flashes of light caused by the beta particles emitted by as they interact with a fluorescing agent added to the benzene. Like gas counters, liquid scintillation counters require shielding and anticoincidence counters. For both the gas proportional counter and liquid scintillation counter, what is measured is the number of beta particles detected in a given time period. Since the mass of the sample is known, this can be converted to a standard measure of activity in units of either counts per minute per gram of carbon (cpm/g C), or
becquerel The becquerel (; symbol: Bq) is the SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or eve ...
s per kg (Bq/kg C, in
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system The metric system is a system of measurement A syste ...
). Each measuring device is also used to measure the activity of a blank sample – a sample prepared from carbon old enough to have no activity. This provides a value for the background radiation, which must be subtracted from the measured activity of the sample being dated to get the activity attributable solely to that sample's . In addition, a sample with a standard activity is measured, to provide a baseline for comparison.Eriksson Stenström et al. (2011), p. 3.

## Accelerator mass spectrometry

AMS counts the atoms of and in a given sample, determining the / ratio directly. The sample, often in the form of graphite, is made to emit C ions (carbon atoms with a single negative charge), which are injected into an accelerator. The ions are accelerated and passed through a stripper, which removes several electrons so that the ions emerge with a positive charge. The ions, which may have from 1 to 4 positive charges (C+ to C4+), depending on the accelerator design, are then passed through a magnet that curves their path; the heavier ions are curved less than the lighter ones, so the different isotopes emerge as separate streams of ions. A particle detector then records the number of ions detected in the stream, but since the volume of (and , needed for calibration) is too great for individual ion detection, counts are determined by measuring the electric current created in a
Faraday cup A Faraday cup is a metal A metal (from Ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts Electrical resistiv ...

.Aitken1990, pp. 82–85. The large positive charge induced by the stripper forces molecules such as , which has a weight close enough to to interfere with the measurements, to dissociate, so they are not detected.Wiebert (1995), p. 16. Most AMS machines also measure the sample's , for use in calculating the sample's radiocarbon age. The use of AMS, as opposed to simpler forms of mass spectrometry, is necessary because of the need to distinguish the carbon isotopes from other atoms or molecules that are very close in mass, such as and . As with beta counting, both blank samples and standard samples are used. Two different kinds of blank may be measured: a sample of dead carbon that has undergone no chemical processing, to detect any machine background, and a sample known as a process blank made from dead carbon that is processed into target material in exactly the same way as the sample which is being dated. Any signal from the machine background blank is likely to be caused either by beams of ions that have not followed the expected path inside the detector or by carbon hydrides such as or . A signal from the process blank measures the amount of contamination introduced during the preparation of the sample. These measurements are used in the subsequent calculation of the age of the sample.

## Calculations

The calculations to be performed on the measurements taken depend on the technology used, since beta counters measure the sample's radioactivity whereas AMS determines the ratio of the three different carbon isotopes in the sample. To determine the age of a sample whose activity has been measured by beta counting, the ratio of its activity to the activity of the standard must be found. To determine this, a blank sample (of old, or dead, carbon) is measured, and a sample of known activity is measured. The additional samples allow errors such as background radiation and systematic errors in the laboratory setup to be detected and corrected for. The most common standard sample material is oxalic acid, such as the HOxII standard, 1,000 lb of which was prepared by the
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is a physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, e ...
(NIST) in 1977 from French beet harvests. The results from AMS testing are in the form of ratios of , , and , which are used to calculate Fm, the "fraction modern". This is defined as the ratio between the / ratio in the sample and the / ratio in modern carbon, which is in turn defined as the / ratio that would have been measured in 1950 had there been no fossil fuel effect. Both beta counting and AMS results have to be corrected for fractionation. This is necessary because different materials of the same age, which because of fractionation have naturally different / ratios, will appear to be of different ages because the / ratio is taken as the indicator of age. To avoid this, all radiocarbon measurements are converted to the measurement that would have been seen had the sample been made of wood, which has a known δ value of −25‰. Once the corrected / ratio is known, a "radiocarbon age" is calculated using: :$\text = - \ln \left(\text\right)\cdot 8033\text$ The calculation uses 8,033 years, the mean-life derived from Libby's half-life of 5,568 years, not 8,267 years, the mean-life derived from the more accurate modern value of 5,730 years. Libby's value for the half-life is used to maintain consistency with early radiocarbon testing results; calibration curves include a correction for this, so the accuracy of final reported calendar ages is assured.

## Errors and reliability

The reliability of the results can be improved by lengthening the testing time. For example, if counting beta decays for 250 minutes is enough to give an error of ± 80 years, with 68% confidence, then doubling the counting time to 500 minutes will allow a sample with only half as much to be measured with the same error term of 80 years.Bowman (1995), pp. 38–39. Radiocarbon dating is generally limited to dating samples no more than 50,000 years old, as samples older than that have insufficient to be measurable. Older dates have been obtained by using special sample preparation techniques, large samples, and very long measurement times. These techniques can allow measurement of dates up to 60,000 and in some cases up to 75,000 years before the present. Radiocarbon dates are generally presented with a range of one
standard deviation In statistics, the standard deviation is a measure of the amount of variation or statistical dispersion, dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected v ...

(usually represented by the Greek letter sigma as 1σ) on either side of the mean. However, a date range of 1σ represents only a 68% confidence level, so the true age of the object being measured may lie outside the range of dates quoted. This was demonstrated in 1970 by an experiment run by the British Museum radiocarbon laboratory, in which weekly measurements were taken on the same sample for six months. The results varied widely (though consistently with a
normal distribution In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by ex ...

of errors in the measurements), and included multiple date ranges (of 1σ confidence) that did not overlap with each other. The measurements included one with a range from about 4250 to about 4390 years ago, and another with a range from about 4520 to about 4690. Errors in procedure can also lead to errors in the results. If 1% of the benzene in a modern reference sample accidentally evaporates, scintillation counting will give a radiocarbon age that is too young by about 80 years.

## Calibration

The calculations given above produce dates in radiocarbon years: i.e. dates that represent the age the sample would be if the / ratio had been constant historically. Although Libby had pointed out as early as 1955 the possibility that this assumption was incorrect, it was not until discrepancies began to accumulate between measured ages and known historical dates for artefacts that it became clear that a correction would need to be applied to radiocarbon ages to obtain calendar dates.Aitken1990, p. 66–67. To produce a curve that can be used to relate calendar years to radiocarbon years, a sequence of securely dated samples is needed which can be tested to determine their radiocarbon age. The study of tree rings led to the first such sequence: individual pieces of wood show characteristic sequences of rings that vary in thickness because of environmental factors such as the amount of rainfall in a given year. These factors affect all trees in an area, so examining tree-ring sequences from old wood allows the identification of overlapping sequences. In this way, an uninterrupted sequence of tree rings can be extended far into the past. The first such published sequence, based on bristlecone pine tree rings, was created by Wesley Ferguson. Hans Suess used this data to publish the first calibration curve for radiocarbon dating in 1967. The curve showed two types of variation from the straight line: a long term fluctuation with a period of about 9,000 years, and a shorter-term variation, often referred to as "wiggles", with a period of decades. Suess said he drew the line showing the wiggles by "cosmic ''schwung''", by which he meant that the variations were caused by extraterrestrial forces. It was unclear for some time whether the wiggles were real or not, but they are now well-established. These short term fluctuations in the calibration curve are now known as de Vries effects, after Hessel de Vries. A calibration curve is used by taking the radiocarbon date reported by a laboratory and reading across from that date on the vertical axis of the graph. The point where this horizontal line intersects the curve will give the calendar age of the sample on the horizontal axis. This is the reverse of the way the curve is constructed: a point on the graph is derived from a sample of known age, such as a tree ring; when it is tested, the resulting radiocarbon age gives a data point for the graph. Over the next thirty years many calibration curves were published using a variety of methods and statistical approaches. These were superseded by the IntCal series of curves, beginning with IntCal98, published in 1998, and updated in 2004, 2009, 2013, and 2020. The improvements to these curves are based on new data gathered from tree rings,
varve 300px, Pleistocene age varves at Scarborough Bluffs, Toronto">Scarborough_Bluffs.html" ;"title="Pleistocene age varves at Scarborough Bluffs">Pleistocene age varves at Scarborough Bluffs, Toronto, Ontario, Canada. The thickest varves are more tha ...
s,
coral Corals are marine invertebrates Marine invertebrates are the invertebrates that live in marine habitats. Invertebrate is a blanket term that includes all animals apart from the vertebrate members of the chordate phylum. Invertebrates lack a vert ...

, plant
macrofossil Macrofossils, also known as megafossils, are preserved organic remains large enough to be visible without a microscope A microscope (from the grc, μικρός, ''mikrós'', "small" and , ''skopeîn'', "to look" or "see") is a laboratory i ...
s,
speleothem A speleothem (; from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 ...
s, and
foraminifera Foraminifera (; Latin for "hole bearers"; informally called "forams") are single-celled organisms, members of a phylum or class (biology), class of Amoeba, amoeboid protists characterized by streaming granular Ectoplasm (cell biology), ectoplasm ...
. The IntCal20 data includes separate curves for the northern and southern hemispheres, as they differ systematically because of the hemisphere effect. The southern curve (SHCAL20) is based on independent data where possible and derived from the northern curve by adding the average offset for the southern hemisphere where no direct data was available. There is also a separate marine calibration curve, MARINE20. For a set of samples forming a sequence with a known separation in time, these samples form a subset of the calibration curve. The sequence can be compared to the calibration curve and the best match to the sequence established. This "wiggle-matching" technique can lead to more precise dating than is possible with individual radiocarbon dates.Walker (2005), pp. 35–37. Wiggle-matching can be used in places where there is a plateau on the calibration curve, and hence can provide a much more accurate date than the intercept or probability methods are able to produce. The technique is not restricted to tree rings; for example, a stratified
tephra Tephra is fragmental material produced by a volcanic eruption Several types of volcanic eruptions—during which lava, tephra (Volcanic ash, ash, lapilli, volcanic bombs and volcanic blocks), and assorted gases are expelled from a Volcan ...

sequence in New Zealand, believed to predate human colonization of the islands, has been dated to 1314 AD ± 12 years by wiggle-matching. The wiggles also mean that reading a date from a calibration curve can give more than one answer: this occurs when the curve wiggles up and down enough that the radiocarbon age intercepts the curve in more than one place, which may lead to a radiocarbon result being reported as two separate age ranges, corresponding to the two parts of the curve that the radiocarbon age intercepted. Bayesian statistical techniques can be applied when there are several radiocarbon dates to be calibrated. For example, if a series of radiocarbon dates is taken from different levels in a stratigraphic sequence, Bayesian analysis can be used to evaluate dates which are outliers and can calculate improved probability distributions, based on the prior information that the sequence should be ordered in time. When Bayesian analysis was introduced, its use was limited by the need to use mainframe computers to perform the calculations, but the technique has since been implemented on programs available for personal computers, such as OxCal.

## Reporting dates

Several formats for citing radiocarbon results have been used since the first samples were dated. As of 2019, the standard format required by the journal ''
'' is as follows. Uncalibrated dates should be reported as ": ± BP", where: * identifies the laboratory that tested the sample, and the sample ID * is the laboratory's determination of the age of the sample, in radiocarbon years * is the laboratory's estimate of the error in the age, at 1σ confidence. * 'BP' stands for "
before present Before Present (BP) years is a time scale used mainly in archaeology Archaeology or archeology is the study of human activity through the recovery and analysis of material culture. Archaeology is often considered a branch of socio-cultural ...
", referring to a reference date of 1950, so that "500 BP" means the year 1450 AD. For example, the uncalibrated date "UtC-2020: 3510 ± 60 BP" indicates that the sample was tested by the Utrecht van der Graaff Laboratorium ("UtC"), where it has a sample number of "2020", and that the uncalibrated age is 3510 years before present, ± 60 years. Related forms are sometimes used: for example, "10 ka BP" means 10,000 radiocarbon years before present (i.e. 8,050 BC), and " yr BP" might be used to distinguish the uncalibrated date from a date derived from another dating method such as
thermoluminescence ''Figure 4'': Illustrated method of passively monitoring sand input (Keizars, 2003). Thermoluminescence is a form of luminescence that is exhibited by certain crystalline materials, such as some minerals, when previously absorbed energy from ...
. Calibrated dates are frequently reported as "cal BP", "cal BC", or "cal AD", again with 'BP' referring to the year 1950 as the zero date. ''Radiocarbon'' gives two options for reporting calibrated dates. A common format is "cal ", where: * is the range of dates corresponding to the given confidence level * indicates the confidence level for the given date range. For example, "cal 1220–1281 AD (1σ)" means a calibrated date for which the true date lies between 1220 AD and 1281 AD, with a confidence level of '1 sigma', or approximately 68%. Calibrated dates can also be expressed as "BP" instead of using "BC" and "AD". The curve used to calibrate the results should be the latest available IntCal curve. Calibrated dates should also identify any programs, such as OxCal, used to perform the calibration. In addition, an article in ''Radiocarbon'' in 2014 about radiocarbon date reporting conventions recommends that information should be provided about sample treatment, including the sample material, pretreatment methods, and quality control measurements; that the citation to the software used for calibration should specify the version number and any options or models used; and that the calibrated date should be given with the associated probabilities for each range.

# Use in archaeology

## Interpretation

A key concept in interpreting radiocarbon dates is
archaeological association This page is a glossary of archaeology Archaeology or archeology is the study of human activity through the recovery and analysis of material culture. Archaeology is often considered a branch of socio-cultural anthropology, but archaeologist ...
: what is the true relationship between two or more objects at an archaeological site? It frequently happens that a sample for radiocarbon dating can be taken directly from the object of interest, but there are also many cases where this is not possible. Metal grave goods, for example, cannot be radiocarbon dated, but they may be found in a grave with a coffin, charcoal, or other material which can be assumed to have been deposited at the same time. In these cases, a date for the coffin or charcoal is indicative of the date of deposition of the grave goods, because of the direct functional relationship between the two. There are also cases where there is no functional relationship, but the association is reasonably strong: for example, a layer of charcoal in a rubbish pit provides a date which has a relationship to the rubbish pit. Contamination is of particular concern when dating very old material obtained from archaeological excavations and great care is needed in the specimen selection and preparation. In 2014,
Thomas Higham Thomas Higham is an archaeological scientist and radiocarbon dating Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties ...
and co-workers suggested that many of the dates published for
Neanderthal Neanderthals (, also Neandertals, ''Homo neanderthalensis'' or ''Homo sapiens neanderthalensis'') are an extinct species In biology Biology is the natural science that studies life and living organisms, including their anatomy, phys ...
artifacts are too recent because of contamination by "young carbon". As a tree grows, only the outermost tree ring exchanges carbon with its environment, so the age measured for a wood sample depends on where the sample is taken from. This means that radiocarbon dates on wood samples can be older than the date at which the tree was felled. In addition, if a piece of wood is used for multiple purposes, there may be a significant delay between the felling of the tree and the final use in the context in which it is found.Bowman (1995), pp. 53–54. This is often referred to as the "" problem. One example is the Bronze Age
trackway Historic roads (historic trail A trail is usually a path, track or unpaved lane or road. In the United Kingdom and the Republic of Ireland, path or footpath is the preferred term for a walking trail. The term is also applied in North Ame ...
at Withy Bed Copse, in England; the trackway was built from wood that had clearly been worked for other purposes before being re-used in the trackway. Another example is driftwood, which may be used as construction material. It is not always possible to recognize re-use. Other materials can present the same problem: for example,
bitumen Asphalt, also known as bitumen (, ), is a sticky, black, highly viscous The viscosity of a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external ...

is known to have been used by some
Neolithic The Neolithic period is the final division of the Stone Age, with a wide-ranging set of developments that appear to have arisen independently in several parts of the world. It is first seen about 12,000 years ago when the first developments of ...
communities to waterproof baskets; the bitumen's radiocarbon age will be greater than is measurable by the laboratory, regardless of the actual age of the context, so testing the basket material will give a misleading age if care is not taken. A separate issue, related to re-use, is that of lengthy use, or delayed deposition. For example, a wooden object that remains in use for a lengthy period will have an apparent age greater than the actual age of the context in which it is deposited.

## Use outside archaeology

Archaeology is not the only field to make use of radiocarbon dating. Radiocarbon dates can also be used in geology, sedimentology, and lake studies, for example. The ability to date minute samples using AMS has meant that palaeobotanists and palaeoclimatologists can use radiocarbon dating directly on pollen purified from sediment sequences, or on small quantities of plant material or charcoal. Dates on organic material recovered from strata of interest can be used to correlate strata in different locations that appear to be similar on geological grounds. Dating material from one location gives date information about the other location, and the dates are also used to place strata in the overall geological timeline. Radiocarbon is also used to date carbon released from ecosystems, particularly to monitor the release of old carbon that was previously stored in soils as a result of human disturbance or climate change. Recent advances in field collection techniques also allow the radiocarbon dating of
methane Methane (, ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Earth ...
and
carbon dioxide Carbon dioxide (chemical formula A chemical formula is a way of presenting information about the chemical proportions of atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is ...

, which are important
greenhouse gas A greenhouse gas (GHG or GhG) is a gas Gas is one of the four fundamental states of matter (the others being solid, liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformat ...
es.

## Notable applications

### Pleistocene/Holocene boundary in Two Creeks Fossil Forest

The
Pleistocene The Pleistocene ( , often referred to as the ''Ice Age'') is the geological epoch In chronology 222px, Joseph Scaliger's ''De emendatione temporum'' (1583) began the modern science of chronology Chronology (from Latin Latin (, or , ) ...
is a geological epoch that began about 2.6 million years ago. The
Holocene The Holocene ( ) is the current geological epoch In geochronology, an epoch is a subdivision of the geologic timescale that is longer than an age (geology), age but shorter than a period (geology), period. The current epoch is the Holocene E ...
, the current geological epoch, begins about 11,700 years ago when the Pleistocene ends.Taylor & Bar-Yosef (2014), pp. 34–37. Establishing the date of this boundary − which is defined by sharp climatic warming − as accurately as possible has been a goal of geologists for much of the 20th century. At Two Creeks, in Wisconsin, a fossil forest was discovered (
Two Creeks Buried Forest State Natural Area Two Creeks Buried Forest State Natural Area is a site in the Wisconsin State Natural Areas Program and a unit of the Ice Age National Scientific Reserve. The site lies in the northeast corner of Manitowoc County, Wisconsin, Manitowoc County on th ...
), and subsequent research determined that the destruction of the forest was caused by the Valders ice readvance, the last southward movement of ice before the end of the Pleistocene in that area. Before the advent of radiocarbon dating, the fossilized trees had been dated by correlating sequences of annually deposited layers of sediment at Two Creeks with sequences in Scandinavia. This led to estimates that the trees were between 24,000 and 19,000 years old, and hence this was taken to be the date of the last advance of the
Wisconsin glaciation The Wisconsin Glacial Episode, also called the Wisconsin glaciation, was the most recent glacial period of the North American ice sheet complex. This advance included the Cordilleran Ice Sheet, which nucleated in the northern North American Cordil ...
before its final retreat marked the end of the Pleistocene in North America.Macdougall (2008), pp. 94–95. In 1952 Libby published radiocarbon dates for several samples from the Two Creeks site and two similar sites nearby; the dates were averaged to 11,404 BP with a standard error of 350 years. This result was uncalibrated, as the need for calibration of radiocarbon ages was not yet understood. Further results over the next decade supported an average date of 11,350 BP, with the results thought to be the most accurate averaging 11,600 BP. There was initial resistance to these results on the part of
Ernst Antevs Ernst Valdemar Antevs (November 20, 1888 – May 19, 1974) was a Swedish-American geologist A geologist is a scientist who studies the solid, liquid, and gaseous matter that constitutes the Earth and other terrestrial planets, as well as the p ...
, the
palaeobotanist Paleobotany, which is also spelled as palaeobotany, is the branch of botany dealing with the recovery and identification of plant remains from geological contexts, and their use for the biological reconstruction of past environments (paleogeogr ...
who had worked on the Scandinavian varve series, but his objections were eventually discounted by other geologists. In the 1990s samples were tested with AMS, yielding (uncalibrated) dates ranging from 11,640 BP to 11,800 BP, both with a standard error of 160 years. Subsequently, a sample from the fossil forest was used in an interlaboratory test, with results provided by over 70 laboratories. These tests produced a median age of 11,788 ± 8 BP (2σ confidence) which when calibrated gives a date range of 13,730 to 13,550 cal BP. The Two Creeks radiocarbon dates are now regarded as a key result in developing the modern understanding of North American glaciation at the end of the Pleistocene.

In 1947,
scrolls '', Vatican Library The Vatican Apostolic Library ( la, Bibliotheca Apostolica Vaticana, it, Biblioteca Apostolica Vaticana), more commonly known as the Vatican Library or informally as the Vat, is the library A library is a curated co ...

were discovered in caves near the
Dead Sea The Dead Sea ( he, יָם הַמֶּלַח lit. Sea of Salt; ar, البحر الميت , lit. ''the Dead Sea'',The first article ''al-'' is unnecessary and usually not used. or Buhayrat, Bahret or Birket Lut, ''lit.'' "Lake/Sea of Lot") is a s ...

that proved to contain writing in
Hebrew Hebrew (, , or ) is a Northwest Semitic languages, Northwest Semitic language of the Afroasiatic languages, Afroasiatic language family. Historically, it is regarded as the language of the Israelites, Judeans and their ancestors. It is the o ...
and
Aramaic Aramaic (: ''Arāmāyā''; : ; : ; ) is a language that originated among the in the ancient , at the end of the , and later became one of the most prominent languages of the . During its three thousand years long history, Aramaic went thr ...
, most of which are thought to have been produced by the
Essenes The Essenes (; Modern Hebrew Modern Hebrew ( he, עברית חדשה, ''ʿivrít ḥadašá ', , ''Literal translation, lit.'' "Modern Hebrew" or "New Hebrew"), also known as Israeli Hebrew or Israeli, and generally referred to by speakers ...
, a small Jewish sect. These scrolls are of great significance in the study of Biblical texts because many of them contain the earliest known version of books of the Hebrew bible.Taylor & Bar-Yosef (2014), pp. 38–42. A sample of the linen wrapping from one of these scrolls, the
Great Isaiah Scroll The Isaiah Scroll, designated 1QIsaa and also known as the Great Isaiah Scroll, is one of the seven Dead Sea Scrolls The Dead Sea Scrolls (also the Qumran Caves Scrolls) are ancient Jewish and Hebrew religious manuscripts that were found in ...

, was included in a 1955 analysis by Libby, with an estimated age of 1,917 ± 200 years. Based on an analysis of the writing style,
palaeographic Palaeography (American and British English spelling differences#Simplification of ae and oe, UK) or paleography (American and British English spelling differences#Simplification of ae and oe, US; ultimately from grc-gre, , ''palaiós'', "old" ...
estimates were made of the age of 21 of the scrolls, and samples from most of these, along with other scrolls which had not been palaeographically dated, were tested by two AMS laboratories in the 1990s. The results ranged in age from the early 4th century BC to the mid 4th century AD. In all but two cases the scrolls were determined to be within 100 years of the palaeographically determined age. The Isaiah scroll was included in the testing and was found to have two possible date ranges at a 2σ confidence level, because of the shape of the calibration curve at that point: there is a 15% chance that it dates from 355 to 295 BC, and an 84% chance that it dates from 210 to 45 BC. Subsequently, these dates were criticized on the grounds that before the scrolls were tested, they had been treated with modern
castor oil Castor oil is a vegetable oil Vegetable oils, or vegetable fats, are oils extracted from seeds or from other parts of fruits. Like animal fats, vegetable fats are ''mixtures'' of triglycerides. Soybean oil, grape seed oil, and cocoa butter are ...

in order to make the writing easier to read; it was argued that failure to remove the castor oil sufficiently would have caused the dates to be too young. Multiple papers have been published both supporting and opposing the criticism.

## Impact

thermoluminescence ''Figure 4'': Illustrated method of passively monitoring sand input (Keizars, 2003). Thermoluminescence is a form of luminescence that is exhibited by certain crystalline materials, such as some minerals, when previously absorbed energy from ...
, optically stimulated luminescence, electron spin resonance, and fission track dating, as well as techniques that depend on annual bands or layers, such as dendrochronology, tephrochronology, and
varve 300px, Pleistocene age varves at Scarborough Bluffs, Toronto">Scarborough_Bluffs.html" ;"title="Pleistocene age varves at Scarborough Bluffs">Pleistocene age varves at Scarborough Bluffs, Toronto, Ontario, Canada. The thickest varves are more tha ...
chronology.Walker (2005), pp. 93–162.

* Astronomical chronology ** Age of the Earth ** Age of the universe * Chronological dating, archaeological chronology ** Absolute dating ** Relative dating ** Phase (archaeology) ** Archaeological association * Geochronology ** Geologic time scale ** Geological history of Earth * 774–775 carbon-14 spike

# Sources

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