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 of radiocarbon (14
C
), a radioactive isotope of carbon.

The method was developed by Willard Libby in the late 1940s and soon became a standard tool for archaeologists. Libby received the Nobel Prize in Chemistry for his work in 1960. The radiocarbon dating method is based on the fact that radiocarbon is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen. The resulting radiocarbon combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire 14
C
by eating the plants. When the animal or plant dies, it stops exchanging carbon with its environment, and from that point onwards the amount of 14
C
it contains begins to decrease as the 14
C
undergoes radioactive decay. Measuring the amount of 14
C
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 14
C
there is to be detected, and because the half-life of 14
C
(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 around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.

The idea behind radiocarbon dating is straightforward, but years of work were required to develop the technique to the point where accurate dates could be obtained. Research has been ongoing since the 1960s to determine what the proportion of 14
C
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 14
C
in different types of organisms (fractionation), and the varying levels of 14
C
throughout the biosphere (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 is substantially longer than the time it takes for its 14
C
to decay below detectable levels, fossil fuels contain almost no 14
C
, and as a result there was a noticeable drop in the proportion of 14
C
in the atmosphere beginning in the late 19th century. Conversely, nuclear testing increased the amount of 14
C
in the atmosphere, which attained a maximum in 1963 of almost twice what it had been before the testing began.

Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying 14
C
atoms in a sample. More recently, accelerator mass spectrometry has become the method of choice; it counts all the 14
C
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. 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 and Bronze Age in different regions.

## Background

### History

In 1939, Martin Kamen and Samuel Ruben 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 14
C
using the laboratory's cyclotron accelerator and soon discovered that the atom's half-life was far longer than had been previously thought. [1] This was followed by a prediction by Serge A. Korff, then employed at the Franklin Institute in Philadelphia, that the interaction of slow neutrons with 14
N
in the upper atmosphere would create 14
C
. [2] [3] It had previously been thought that 14
C
would be more likely to be created by deuterons interacting with 13
C
. [1] At some time during World War II, Willard Libby, who was then at Berkeley, learned of Korff's research and conceived the idea that it might be possible to use radiocarbon for dating. [2] [4]

In 1945, Libby moved to the University of Chicago 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 14
C
as well as non-radioactive carbon. [5] [6] Libby and several collaborators proceeded to experiment with methane collected from sewage works in Baltimore, and after isotopically enriching their samples they were able to demonstrate that they contained radioactive 14
C
. By contrast, methane created from petroleum showed no radiocarbon activity because of its age. The results were summarized in a paper in Science in 1947, in which the authors commented that their results implied it would be possible to date materials containing carbon of organic origin. [5] [7]

Libby and James Arnold 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, 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 1949. [8] [9] Within 11 years of their announcement, more than 20 radiocarbon dating laboratories had been set up worldwide. [10]

In 1960, Libby was awarded the Nobel Prize in Chemistry for this work. [5]

### Physical and chemical details

In nature, carbon exists as two stable, nonradioactive isotopes: carbon-12 (12
C
), and carbon-13 (13
C
), and a radioactive isotope, carbon-14 (14
C
), also known as "radiocarbon". The half-life of 14
C
(the time it takes for half of a given amount of 14
C
to decay) is about 5,730 years, so its concentration in the atmosphere might be expected to reduce over thousands of years, but 14
C
is constantly being produced in the lower stratosphere and upper troposphere by cosmic rays, which generate neutrons that in turn create 14
C
when they strike nitrogen-14 (14
N
) atoms. [5] The following nuclear reaction creates 14
C
:

n + 14
7
N
14
6
C
+ p

where n represents a neutron and p represents a proton. [11]

Once produced, the 14
C
quickly combines with the oxygen in the atmosphere to form carbon dioxide (CO
2
). Carbon dioxide produced in this way diffuses in the atmosphere, is dissolved in the ocean, and is taken up by plants via photosynthesis. Animals eat the plants, and ultimately the radiocarbon is distributed throughout the biosphere. The ratio of 14
C
to 12
C
is approximately 1.5 parts of 14
C
to 1012 parts of 12
C
. [12] In addition, about 1% of the carbon atoms are of the stable isotope 13
C
. [5]

The equation for the radioactive decay of 14
C
is: [13]

14
6
C
14
7
N
+
e
+
ν
e

By emitting a beta particle (an electron, e) and an electron antineutrino (
ν
e
), one of the neutrons in the 14
C
nucleus changes to a proton and the 14
C
nucleus reverts to the stable (non-radioactive) isotope 14
N
. [14]

### Principles

During its life, a plant or animal is exchanging carbon with its surroundings, so the carbon it contains will have the same proportion of 14
C
as the atmosphere. Once it dies, it ceases to acquire 14
C
, but the 14
C
within its biological material at that time will continue to decay, and so the ratio of 14
C
to 12
C
in its remains will gradually decrease. Because 14
C
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 14
C
will be left. [12]

The equation governing the decay of a radioactive isotope is: [5]

${\displaystyle N=N_{0}e^{-\lambda t}\,}$

where N0 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. [5] λ is a constant that depends on the particular isotope; for a given isotope it is equal to the reciprocal of the mean-life – i.e. the average or expected time a given atom will survive before undergoing radioactive decay. [5] The mean-life, denoted by τ, of 14
C
is 8,267 years, so the equation above can be rewritten as: [15]

${\displaystyle t=8267\cdot \ln(N_{0}/N){\text{ years}}}$

The sample is assumed to have originally had the same 14
C
/12
C
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 N0, the number of 14
C
atoms in the original sample. Measurement of N, the number of 14
C
atoms currently in the sample, allows the calculation of t, the age of the sample, using the equation above. [12]

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 14
C
's half-life than its mean-life. [note 1] The currently accepted value for the half-life of 14
C
is 5,730 years. [5] This means that after 5,730 years, only half of the initial 14
C
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 14
C
in the atmosphere has remained constant over time. [5] In fact, the level of 14
C
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. [16] This is done by calibration curves, which convert a measurement of 14
C
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 14
C
/12
C
ratio has not changed over time. Calculating radiocarbon ages also requires the value of the half-life for 14
C
, which for more than a decade after Libby's initial work was thought to be 5,568 years. This was revised in the early 1960s to 5,730 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, and to avoid the risk of a double correction for the incorrect half-life, radiocarbon ages are still calculated using the incorrect half-life value. A correction for the half-life is incorporated into calibration curves, so even though radiocarbon ages are calculated using a half-life value that is known to be incorrect, the final reported calibrated date, in calendar years, is accurate. 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 14
C
, and because no correction (calibration) has been applied for the historical variation of 14
C
in the atmosphere over time. [17] [18] [note 2]

### Carbon exchange reservoir

Simplified version of the carbon exchange reservoir, showing proportions of carbon and relative activity of the 14
C
in each reservoir [5] [note 3]

Carbon is distributed throughout the atmosphere, the biosphere, and the oceans; these are referred to collectively as the carbon exchange reservoir, [21] 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 14
C
generated by cosmic rays to fully mix with them. This affects the ratio of 14
C
to 12
C
in the different reservoirs, and hence the radiocarbon ages of samples that originated in each reservoir. [5] The atmosphere, which is where 14
C
is generated, contains about 1.9% of the total carbon in the reservoirs, and the 14
C
it contains mixes in less than seven years. [20] [22] The ratio of 14
C
to 12
C
in the atmosphere is taken as the baseline for the other reservoirs: if another reservoir has a lower ratio of 14
C
to 12
C
, it indicates that the carbon is older and hence that some of the 14
C
has decayed. [16] The ocean surface is an example: it contains 2.4% of the carbon in the exchange reservoir, [20] but there is only about 95% as much 14
C
as would be expected if the ratio were the same as in the atmosphere. [5] The time it takes for carbon from the atmosphere to mix with the surface ocean is only a few years, [23] but the surface waters also receive water from the deep ocean, which has more than 90% of the carbon in the reservoir. [16] 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 14
C
, and water recently at the surface, with 14
C
in equilibrium with the atmosphere. [16]

Creatures living at the ocean surface have the same 14
C
ratios as the water they live in, and as a result of the reduced 14
C
/12
C
ratio, the radiocarbon age of marine life is typically about 440 years. [24] [25] [note 4] Organisms on land are in closer equilibrium with the atmosphere and have the same 14
C
/12
C
ratio as the atmosphere. [5] 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 on the diagram. [20] 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 14
C
/12
C
ratio lower than that of the biosphere. [5]

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