Radiocarbon dating

Radiocarbon 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. It is based on the fact that radiocarbon is constantly being created in the Earth's atmosphere by the interaction of cosmic rays with atmospheric nitrogen. The resulting combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; 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. 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. The half-life of is about 5,730 years, so the oldest dates that can be reliably measured by this process date to approximately 50,000 years ago, although special preparation methods occasionally make an accurate analysis of older samples possible. Libby received the Nobel Prize in Chemistry 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, and the varying levels of throughout the biosphere. 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 their 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 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 emitted by decaying atoms in a sample. More recently, accelerator mass spectrometry 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, 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 using the laboratory's cyclotron accelerator and soon discovered that the atom's half-life was far longer than had been previously thought. 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 in the upper atmosphere would create. It had previously been thought that would be more likely to be created by deuterons interacting with. 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.
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 as well as non-radioactive carbon. 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. 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.
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 ± 75 years, were dated by radiocarbon measurement to an average of 2800 BC ± 250 years. These results were published in Science in December 1949. 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 for this work.

Physical and chemical details

In nature, carbon exists as three isotopes. Two are stable and not radioactive: carbon-12, and carbon-13 ; and carbon-14, also known as "radiocarbon", which is radioactive. The half-life of 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 and upper troposphere, primarily by galactic cosmic rays, 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 atoms and turn them into. The following nuclear reaction is the main pathway by which is created:
where n represents a neutron and p represents a proton.
Once produced, the quickly combines with the oxygen in the atmosphere to form first carbon monoxide, and ultimately carbon dioxide.
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 to is approximately 1.25 parts of to 10¹² parts of. 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 and an electron antineutrino, one of the neutrons in the nucleus changes to a proton and the nucleus reverts to the stable 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:
where N₀ is the number of atoms of the isotope in the original sample, 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 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:
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 N₀, 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 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 5,700 ± 30 years. This means that after 5,700 years, only half of the initial will remain; a quarter will remain after 11,400 years; an eighth after 17,100 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. This is done by calibration curves, 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. For consistency with these early papers, it was agreed at the 1962 Radiocarbon Conference in Cambridge 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 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 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 has been applied for the historical variation of in the atmosphere over time.