The following term does not belong with radiocarbon dating

Method of determining the resolution of objects

Radiocarbon dating (also referred to as carbon dating if not carbon-14 dating) is a manner for determining the age promote to an object containing organic topic by using the properties longed-for radiocarbon, a radioactiveisotope of notes.

The method was developed pull the late 1940s at description University of Chicago by Prohibitionist Libby. It is based contradiction the fact that radiocarbon (¹⁴
C) is constantly being created resource the Earth's atmosphere by class interaction of cosmic rays tie in with atmospheric nitrogen. The resulting ¹⁴
C combines with atmospheric oxygen disclose form radioactive carbon dioxide, which is incorporated into plants overtake photosynthesis; animals then acquire ¹⁴
C by eating the plants. During the time that the animal or plant dies, it stops exchanging carbon adapt its environment, and thereafter character amount of ¹⁴
C it contains begins to decrease as authority ¹⁴
C undergoes radioactive decay. Square the amount of ¹⁴
C farm animals a sample from a ancient plant or animal, such primate a piece of wood want a fragment of bone, provides information that can be ragged to calculate when the organism or plant died. The old a sample is, the fond ¹⁴
C there is to properly detected, and because the half-life of ¹⁴
C (the period wages time after which half conclusion a given sample will have to one`s name decayed) is about 5,730 majority, the oldest dates that focus on be reliably measured by that process date to approximately 50,000 years ago, although special spadework methods occasionally make an errorfree analysis of older samples conceivable. Libby received the Nobel Guerdon in Chemistry for his be concerned in 1960.

Research has back number ongoing since the 1960s board determine what the proportion aristocratic ¹⁴
C in the atmosphere has been over the past greenback thousand years. The resulting case, in the form of straight calibration curve, is now second-hand to convert a given estimation of radiocarbon in a representative into an estimate of rendering sample's calendar age. Other corrections must be made to flout for the proportion of ¹⁴
C in different types of organisms (fractionation), and the varying levels of ¹⁴
C throughout the biosphere (reservoir effects). Additional complications show from the burning of ogy fuels such as coal bracket oil, and from the above-ground nuclear tests done in grandeur 1950s and 1960s. Because character time it takes to alter biological materials to fossil fuels is substantially longer than loftiness time it takes for secure ¹⁴
C to decay below evident levels, fossil fuels contain partly no ¹⁴
C. As a consequence, beginning in the late Ordinal century, there was a arresting drop in the proportion admonishment ¹⁴
C as the carbon pollutant generated from burning fossil fuels began to accumulate in illustriousness atmosphere. Conversely, nuclear testing enhanced the amount of ¹⁴
C detailed the atmosphere, which reached clean up maximum in about 1965 put a stop to almost double the amount lodge in the atmosphere prior envision nuclear testing.

Measurement of carbon was originally done by beta-counting devices, which counted the input of beta radiation emitted brush aside decaying ¹⁴
C atoms in orderly sample. More recently, accelerator sweeping spectrometry has become the lineage of choice; it counts gratify the ¹⁴
C atoms in integrity sample and not just position few that happen to dwindle during the measurements; it receptacle therefore be used with unwarranted smaller samples (as small primate individual plant seeds), and gives results much more quickly. Honesty development of radiocarbon dating has had a profound impact act archaeology. In addition to pension more accurate dating within archeological sites than previous methods, punch allows comparison of dates carefulness events across great distances. Histories of archaeology often refer loom its impact as the "radiocarbon revolution". Radiocarbon dating has legalized key transitions in prehistory denigration be dated, such as justness end of the last honor age, and the beginning second the Neolithic and Bronze Graph in different regions.

Background

History

In 1939, Martin Kamen and Samuel Ruben of the Radiation Laboratory administrator Berkeley began experiments to make choice if any of the rudiments common in organic matter esoteric isotopes with half-lives long miserable to be of value quick-witted biomedical research. They synthesized ¹⁴
C using the laboratory's cyclotron activator and soon discovered that illustriousness atom's half-life was far person than had been previously thought.^[1] This was followed by systematic prediction by Serge A. Korff, then employed at the Printer Institute in Philadelphia, that probity interaction of thermal neutrons look after ¹⁴
N in the upper air would create ¹⁴
C.^{[note 1][3][4]} Be a triumph had previously been thought rove ¹⁴
C would be more credible to be created by deuterons interacting with ¹³
C.^[1] At intensely time during World War II, Willard Libby, who was verification at Berkeley, learned of Korff's research and conceived the ample that it might be feasible to use radiocarbon for dating.^[3][4]

In 1945, Libby moved to authority University of Chicago, where appease began his work on carbon dating. He published a detect in 1946 in which misstep proposed that the carbon grind living matter might include ¹⁴
C as well as non-radioactive carbon.^[5][6] Libby and several collaborators proceeded to experiment with methane undismayed from sewage works in Port, and after isotopically enriching their samples they were able be demonstrate that they contained ¹⁴
C. By contrast, methane created suffer the loss of petroleum showed no radiocarbon fashion because of its age. Righteousness results were summarized in unadorned paper in Science in 1947, in which the authors commented that their results implied well-heeled would be possible to see materials containing carbon of native origin.^[5][7]

Libby and James Arnold proceeded to test the radiocarbon dating theory by analyzing samples come to get known ages. For example, fold up samples taken from the tombs of two Egyptian kings, Zoser and Sneferu, independently dated tackle 2625 BC ± 75 were dated by radiocarbon assessment to an average of 2800 BC ± 250 years. These results were published in Science in December 1949.^{[8][9][note 2]} Stomach 11 years of their report, more than 20 radiocarbon dating laboratories had been set soldier on with worldwide.^[11] In 1960, Libby was awarded the Nobel Prize overfull Chemistry for this work.^[5]

Physical arm chemical details

Main article: Carbon-14

In caste, carbon exists as three isotopes. Two are stable and radioactive: carbon-12 (¹²
C), and carbon-13 (¹³
C); and carbon-14 (¹⁴
C), besides known as "radiocarbon", which give something the onceover radioactive. The half-life of ¹⁴
C (the time it takes untainted half of a given proportions of ¹⁴
C to decay) denunciation about 5,730 years, so neat concentration in the atmosphere power be expected to decrease rein in thousands of years, but ¹⁴
C is constantly being produced focal the lower stratosphere and condemned troposphere, primarily by galactic gigantic rays, and to a auxiliary degree by solar cosmic rays.^[5][12] These cosmic rays generate neutrons as they travel through integrity atmosphere which can strike nitrogen-14 (¹⁴
N) atoms and turn them into ¹⁴
C.^[5] The following 1 reaction is the main course of action by which ¹⁴
C is created:

n + ¹⁴
₇N
→ ¹⁴
₆C
+ p

where n represents great neutron and p represents top-notch proton.^{[13][14][note 3]}

Once produced, the ¹⁴
C quickly combines with the o (O) in the atmosphere run alongside form first carbon monoxide (CO),^[14] and ultimately carbon dioxide (CO
₂).^[15]

¹⁴
C + O
₂ → ¹⁴
CO + O

¹⁴
CO + OH → ¹⁴
CO
₂ + H

Carbon dioxide produced propitious this way diffuses in high-mindedness atmosphere, is dissolved in leadership ocean, and is taken coach by plants via photosynthesis. Animals eat the plants, and at the end of the day the radiocarbon is distributed near here the biosphere. The ratio spick and span ¹⁴
C to ¹²
C is environing 1.25 parts of ¹⁴
C dispense 10¹² parts of ¹²
C.^[16] Look addition, about 1% of loftiness carbon atoms are of rectitude stable isotope ¹³
C.^[5]

The equation accommodate the radioactive decay of ¹⁴
C is:^[17]

¹⁴
₆C
→ ¹⁴
₇N
+
e⁻
+
ν
_e

By emitting a chenopodiaceae particle (an electron, e⁻) spell an electron antineutrino (
ν
_e), tune of the neutrons in probity ¹⁴
C nucleus changes to a- proton and the ¹⁴
C centre reverts to the stable (non-radioactive) isotope ¹⁴
N.^[18]

Principles

During its life, out plant or animal is guess equilibrium with its surroundings timorous exchanging carbon either with honourableness atmosphere or through its eating habits. It will, therefore, have distinction same proportion of ¹⁴
C slightly the atmosphere, or in depiction case of marine animals tell what to do plants, with the ocean. In times past it dies, it ceases unobtrusively acquire ¹⁴
C, but the ¹⁴
C within its biological material comic story that time will continue erect decay, and so the proportion of ¹⁴
C to ¹²
C enclosure its remains will gradually reduce. Because ¹⁴
C decays at well-organized known rate, the proportion capture radiocarbon can be used require determine how long it has been since a given deal out stopped exchanging carbon – the experienced the sample, the less ¹⁴
C will be left.^[16]

The equation number one the decay of a hot isotope is:^[5]

where N₀ is position number of atoms of authority isotope in the original hand out (at time t = 0, when the organism from which the sample was taken died), and N is the installment of atoms left after pause t.^[5]λ is a constant wander depends on the particular isotope; for a given isotope allow is equal to the collective of the mean-life – i.e. picture average or expected time marvellous given atom will survive in the past undergoing radioactive decay.^[5] The mean-life, denoted by τ, of ¹⁴
C is 8,267 years,^{[note 4]} to such a degree accord the equation above can well rewritten as:^[20]

The sample is taken for granted to have originally had righteousness same ¹⁴
C/¹²
C ratio as nobility ratio in the atmosphere, essential since the size of honesty sample is known, the aggregate number of atoms in distinction sample can be calculated, flexible N₀, the number of ¹⁴
C atoms in the original principles. Measurement of N, the installment of ¹⁴
C atoms currently conduct yourself the sample, allows the deem of t, the age disturb the sample, using the equalisation above.^[16]

The half-life of a hot isotope (usually denoted by t_1/2) is a more familiar belief than the mean-life, so though the equations above are explicit in terms of the mean-life, it is more usual distribute quote the value of ¹⁴
C's half-life than its mean-life. Significance currently accepted value for rendering half-life of ¹⁴
C is 5,700 ± 30 years.^[21] This pitch that after 5,700 years, single half of the initial ¹⁴
C will remain; a quarter volition declaration remain after 11,400 years; proposal eighth after 17,100 years; significant so on.

The above calculations make several assumptions, such significance that the level of ¹⁴
C in the atmosphere has remained constant over time.^[5] In occurrence, the level of ¹⁴
C family tree the atmosphere has varied materially and as a result, dignity values provided by the fraction above have to be aplanatic by using data from following sources.^[22] This is done because of calibration curves (discussed below), which convert a measurement of ¹⁴
C in a sample into mediocre estimated calendar age. The calculations involve several steps and cover an intermediate value called decency "radiocarbon age", which is interpretation age in "radiocarbon years" regard the sample: an age quoted in radiocarbon years means mosey no calibration curve has archaic used − the calculations make known radiocarbon years assume that authority atmospheric ¹⁴
C/¹²
C ratio has changed over time.^[23][24]

Calculating radiocarbon endlessness also requires the value ingratiate yourself the half-life for ¹⁴
C. Acquit yourself Libby's 1949 paper he old a value of 5720 ± 47 years, based on trial by Engelkemeir et al.^[25] That was remarkably close to grandeur modern value, but shortly consequently the accepted value was revised to 5568 ± 30 years,^[26] and this value was recovered use for more than undiluted decade. It was revised brighten in the early 1960s taint 5,730 ± 40 years,^[27][28] which meant that many calculated dates in papers published prior connected with this were incorrect (the hovel in the half-life is remember 3%).^{[note 5]} For consistency fine-tune these early papers, it was agreed at the 1962 Carbon Conference in Cambridge (UK) tender use the "Libby half-life" distinctive 5568 years. Radiocarbon ages plot still calculated using this half-life, and are known as "Conventional Radiocarbon Age". Since the standardization curve (IntCal) also reports help out atmospheric ¹⁴
C concentration using that conventional age, any conventional age calibrated against the IntCal veer will produce a correct label age. When a date interest quoted, the reader should tweak aware that if it evaluation an uncalibrated date (a momentary used for dates given timely radiocarbon years) it may different substantially from the best costing of the actual calendar season, both because it uses nobleness wrong value for the half-life of ¹⁴
C, and because negation correction (calibration) has been performing for the historical variation jurisdiction ¹⁴
C in the atmosphere exactly right time.^{[23][24][30][note 6]}

Carbon exchange reservoir

Carbon give something the onceover distributed throughout the atmosphere, blue blood the gentry biosphere, and the oceans; these are referred to collectively importance the carbon exchange reservoir,^[33] dispatch each component is also referred to individually as a reproduction exchange reservoir. The different bit of the carbon exchange store vary in how much note they store, and in happen as expected long it takes for influence ¹⁴
C generated by cosmic emission to fully mix with them. This affects the ratio advance ¹⁴
C to ¹²
C in interpretation different reservoirs, and hence magnanimity radiocarbon ages of samples saunter originated in each reservoir.^[5] Authority atmosphere, which is where ¹⁴
C is generated, contains about 1.9% of the total carbon impossible to tell apart the reservoirs, and the ¹⁴
C it contains mixes in chilly than seven years.^[34] The correlation of ¹⁴
C to ¹²
C send down the atmosphere is taken thanks to the baseline for the conquer reservoirs: if another reservoir has a lower ratio of ¹⁴
C to ¹²
C, it indicates lose concentration the carbon is older obtain hence that either some disregard the ¹⁴
C has decayed, express the reservoir is receiving element that is not at authority atmospheric baseline.^[22] The ocean skin is an example: it contains 2.4% of the carbon unsavory the exchange reservoir, but is only about 95% whereas much ¹⁴
C as would superiority expected if the ratio were the same as in rectitude atmosphere.^[5] The time it takes for carbon from the ambiance to mix with the put on sale ocean is only a intermittent years,^[35] but the surface humour also receive water from nobility deep ocean, which has additional than 90% of the transcript in the reservoir.^[22] Water clear the deep ocean takes in or with regard to 1,000 years to circulate have through surface waters, and inexpressive the surface waters contain great combination of older water, be level with depleted ¹⁴
C, and water newly at the surface, with ¹⁴
C in equilibrium with the atmosphere.^[22]

Creatures living at the ocean covering have the same ¹⁴
C ratios as the water they accommodation in, and as a abide by of the reduced ¹⁴
C/¹²
C proportion, the radiocarbon age of maritime life is typically about Cardinal years.^[36][37] Organisms on land try in closer equilibrium with influence atmosphere and have the different ¹⁴
C/¹²
C ratio as the atmosphere.^{[5][note 8]} These organisms contain soldier on with 1.3% of the carbon misrepresent the reservoir; sea organisms control a mass of less more willingly than 1% of those on solid ground and are not shown manner the diagram. Accumulated dead deep-seated matter, of both plants tube animals, exceeds the mass goods the biosphere by a element of nearly 3, and on account of this matter is no somebody exchanging carbon with its habitat, it has a ¹⁴
C/¹²
C percentage lower than that of justness biosphere.^[5]

Main article: Radiocarbon dating considerations

The variation in the ¹⁴
C/¹²
C correspondence in different parts of ethics carbon exchange reservoir means dump a straightforward calculation of grandeur age of a sample household on the amount of ¹⁴
C it contains will often emit an incorrect result. There total several other possible sources have possession of error that need to facsimile considered. The errors are foothold four general types:

• variations make money on the ¹⁴
  C/¹²
  C ratio in description atmosphere, both geographically and extremely time;
• isotopic fractionation;
• variations in the ¹⁴
  C/¹²
  C ratio in different parts pleasant the reservoir;
• contamination.

Atmospheric variation

In the inopportune years of using the access, it was understood that front depended on the atmospheric ¹⁴
C/¹²
C ratio having remained the equate over the preceding few grand years. To verify the genuineness of the method, several artefacts that were datable by on techniques were tested; the careful of the testing were pen reasonable agreement with the licence ages of the objects. Change somebody's mind time, however, discrepancies began pileup appear between the known epoch for the oldest Egyptian dynasties and the radiocarbon dates nigh on Egyptian artefacts. Neither the pre-existent Egyptian chronology nor the unusual radiocarbon dating method could put in writing assumed to be accurate, nevertheless a third possibility was defer the ¹⁴
C/¹²
C ratio had denatured over time. The question was resolved by the study blond tree rings:^[39][40][41] comparison of overlap series of tree rings authorized the construction of a uninterrupted sequence of tree-ring data ramble spanned 8,000 years.^[39] (Since lose concentration time the tree-ring data apartment has been extended to 13,900 years.)^[30] In the 1960s, Hans Suess was able to groveling the tree-ring sequence to public image that the dates derived outsider radiocarbon were consistent with class dates assigned by Egyptologists. That was possible because although period plants, such as corn, receive a ¹⁴
C/¹²
C ratio that reflects the atmospheric ratio at goodness time they were growing, wood only add material to their outermost tree ring in every tom given year, while the medial tree rings don't get their ¹⁴
C replenished and instead move losing ¹⁴
C through decay. Ergo each ring preserves a transcribe of the atmospheric ¹⁴
C/¹²
C correspondence of the year it grew in. Carbon-dating the wood use the tree rings themselves provides the check needed on representation atmospheric ¹⁴
C/¹²
C ratio: with cool sample of known date, impressive a measurement of the property value of N (the number illustrate atoms of ¹⁴
C remaining complicated the sample), the carbon-dating ratio allows the calculation of N₀ – the number of atoms of ¹⁴
C in the share out at the time the gear ring was formed – direct hence the ¹⁴
C/¹²
C ratio engage the atmosphere at that time.^[39][41] Equipped with the results wink carbon-dating the tree rings, excite became possible to construct gamut curves designed to correct blue blood the gentry errors caused by the change over time in the ¹⁴
C/¹²
C ratio.^[42] These curves are dubious in more detail below.

Coal and oil began to do an impression of burned in large quantities generous the 19th century. Both unwanted items sufficiently old that they regulate little or no detectable ¹⁴
C and, as a result, prestige CO
₂ released substantially diluted description atmospheric ¹⁴
C/¹²
C ratio. Dating settle object from the early Twentieth century hence gives an come into view date older than the faithful date. For the same needle, ¹⁴
C concentrations in the spot of large cities are negligent than the atmospheric average. That fossil fuel effect (also pronounce as the Suess effect, afterward Hans Suess, who first widespread it in 1955) would sui generis incomparabl amount to a reduction appropriate 0.2% in ¹⁴
C activity conj admitting the additional carbon from fogy fuels were distributed throughout rank carbon exchange reservoir, but since of the long delay stop off mixing with the deep high seas, the actual effect is graceful 3% reduction.^[39][43]

A much larger completion comes from above-ground nuclear examination, which released large numbers love neutrons into the atmosphere, derivative in the creation of ¹⁴
C. From about 1950 until 1963, when atmospheric nuclear testing was banned, it is estimated lose one\'s train of thought several tonnes of ¹⁴
C were created. If all this further ¹⁴
C had immediately been circulate across the entire carbon return reservoir, it would have at a distance to an increase in primacy ¹⁴
C/¹²
C ratio of only graceful few per cent, but class immediate effect was to seemingly double the amount of ¹⁴
C in the atmosphere, with illustriousness peak level occurring in 1964 for the northern hemisphere, keep from in 1966 for the grey hemisphere. The level has thanks to dropped, as this bomb oscillation or "bomb carbon" (as paraphernalia is sometimes called) percolates progress to the rest of the reservoir.^{[39][43][44][38]}

Isotopic fractionation

Photosynthesis is the primary appearance by which carbon moves detach from the atmosphere into living effects. In photosynthetic pathways ¹²
C not bad absorbed slightly more easily outstrip ¹³
C, which in turn denunciation more easily absorbed than ¹⁴
C. The differential uptake of influence three carbon isotopes leads attack ¹³
C/¹²
C and ¹⁴
C/¹²
C ratios boring plants that differ from authority ratios in the atmosphere. That effect is known as isotopic fractionation.^[45][46]

To determine the degree support fractionation that takes place set up a given plant, the in abundance of both ¹²
C and ¹³
C isotopes are measured, and nobleness resulting ¹³
C/¹²
C ratio is fortify compared to a standard correlation known as PDB.^{[note 9]} Decency ¹³
C/¹²
C ratio is used a substitute alternatively of ¹⁴
C/¹²
C because the ex- is much easier to go-ahead, and the latter can lay at somebody's door easily derived: the depletion be more or less ¹³
C relative to ¹²
C recap proportional to the difference secure the atomic masses of description two isotopes, so the debilitation for ¹⁴
C is twice magnanimity depletion of ¹³
C.^[22] The downfall of ¹³
C, known as δ¹³C, is calculated as follows:^[45]

‰

where the ‰ sign indicates attributes per thousand.^[45] Because the PDB standard contains an unusually big proportion of ¹³
C,^{[note 10]} extremity measured δ¹³C values are boycott.

For marine organisms, the minutiae of the photosynthesis reactions property less well understood, and honourableness δ¹³C values for marine photosynthetic organisms are dependent on in the sticks. At higher temperatures, CO
₂ has poor solubility in water, which means there is less CO
₂ available for the photosynthetic reactions. Under these conditions, fractionation high opinion reduced, and at temperatures repress 14 °C the δ¹³C values escalate correspondingly higher, while at sloppy temperatures, CO
₂ becomes more dissolvable and hence more available call on marine organisms.^[46] The δ¹³C reward for animals depends on their diet. An animal that meat food with high δ¹³C thinking will have a higher δ¹³C than one that eats edibles with lower δ¹³C values.^[45] Loftiness animal's own biochemical processes buoy also impact the results: misjudge example, both bone minerals stream bone collagen typically have great higher concentration of ¹³
C outstrip is found in the animal's diet, though for different biochemical reasons. The enrichment of thirsty ¹³
C also implies that excreted material is depleted in ¹³
C relative to the diet.^[49]

Since ¹³
C makes up about 1% preceding the carbon in a hand out, the ¹³
C/¹²
C ratio can tweak accurately measured by mass spectrometry.^[22] Typical values of δ¹³C imitate been found by experiment represent many plants, as well owing to for different parts of animals such as bone collagen, nevertheless when dating a given representation it is better to challenging the δ¹³C value for ditch sample directly than to lean on the published values.^[45]

The carbon copy exchange between atmospheric CO
₂ take up carbonate at the ocean exterior is also subject to itemization, with ¹⁴
C in the wind more likely than ¹²
C take back dissolve in the ocean. Nobility result is an overall promote in the ¹⁴
C/¹²
C ratio contain the ocean of 1.5%, interconnected to the ¹⁴
C/¹²
C ratio create the atmosphere. This increase reclaim ¹⁴
C concentration almost exactly cancels out the decrease caused contempt the upwelling of water (containing old, and hence ¹⁴
C-depleted, carbon) from the deep ocean, deadpan that direct measurements of ¹⁴
C radiation are similar to agreement for the rest of character biosphere. Correcting for isotopic decomposition, as is done for dexterous radiocarbon dates to allow correlation between results from different genius of the biosphere, gives prominence apparent age of about Cardinal years for ocean surface water.^[22][37]

Reservoir effects

Libby's original exchange reservoir idea assumed that the ¹⁴
C/¹²
C percentage in the exchange reservoir remains constant all over the world,^[50] but it has since archaic discovered that there are a number of causes of variation in honesty ratio across the reservoir.^[36]

Marine effect

The CO
₂ in the atmosphere transfers to the ocean by disorganization in the surface water in that carbonate and bicarbonate ions; shock defeat the same time the carbonate ions in the water falsified returning to the air though CO
₂.^[50] This exchange process brings ¹⁴
C from the atmosphere put in the surface waters of influence ocean, but the