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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, a radioactive isotope of carbon.

The method was developed in the late 1940s at the University of Chicago by Willard Libby, who received the Nobel Prize in Chemistry for his work in 1960. It is based on the fact that radiocarbon (14
C
) is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen. The resulting 14
C
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 thereafter 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 approximately 50,000 years ago, although special preparation methods occasionally make accurate analysis of older samples possible.

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
. As a result, beginning in the late 19th century, there was a noticeable drop in the proportion of 14
C
as the carbon dioxide generated from burning fossil fuels began to accumlate in the atmosphere. Conversely, nuclear testing increased the amount of 14
The method was developed in the late 1940s at the University of Chicago by Willard Libby, who received the Nobel Prize in Chemistry for his work in 1960. It is based on the fact that radiocarbon (14
C
) is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen. The resulting 14
C
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 thereafter 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 approximately 50,000 years ago, although special preparation methods occasionally make accurate analysis of older samples possible.

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
. As a result, beginning in the late 19th century, there was a noticeable drop in the proportion of 14
C
as the carbon dioxide generated from burning fossil fuels began to accumlate in the atmosphere. Conversely, nuclear testing increased the amount of 14
C
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 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.

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 thermal neutrons with 14
N
in the upper atmosphere would create 14
C
.[note 1][3][4] 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.[3][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 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 December 1949.[8][9][note 2] Within 11 years of their announcement, more than 20 radiocarbon dating laboratories had been set up worldwide.[11] 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 decrease over thousands of years, but 14
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 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 December 1949.[8][9][note 2] Within 11 years of their announcement, more than 20 radiocarbon dating laboratories had been set up worldwide.[11] In 1960, Libby was awarded the Nobel Prize in Chemistry for this work.[5]

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 decrease over thousands of years, but 14
C
is constantly being produced in the lower stratosphere and upper troposphere, primarily by galactic cosmic rays, and to a lesser degree by solar cosmic rays.[5][12] These cosmic rays generate neutrons as they travel through the atmosphere which can strike nitrogen-14 (14
N
) atoms and turn them into 14
C
.[5] The following nuclear reaction is the main pathway by which 14
C
is created:

n + 14
7
Nneutron and p represents a proton.[13][14][note 3]

Once produced, the 14
C
quickly combines with the oxygen in the atmosphere to form first carbon monoxide (CO),[14] and ultimately carbon dioxide (CO
2
).[15]

14
14
C
quickly combines with the oxygen in the atmosphere to form first carbon monoxide (CO),[14] and ultimately carbon dioxide (CO
2
).[15]

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 1.25 parts of 14
C
to 1012 parts of 12
C
.[16] 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:[17]

14
6
C
14
7
N
+ 14
C
is:[17]

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
.[18]

### 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 14
C
as the atmosphere, or in the case of marine animals or plants, with the ocean. 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
as the atmosphere, or in the case of marine animals or plants, with the ocean. 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.[16]

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