page_title: Radiocarbon dating
section_title: Isotopic fractionation
hierarchical_section_title: Radiocarbon dating / Dating considerations / Isotopic fractionation
caption_attribution_description: North Ronaldsay sheep. The sheep are a rare breed which has evolved to eat seaweed. All access to the shore is fenced to stop them getting onto pastures as their digestive systems cannot cope with grass, due to the high copper content.
context_page_description: 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, who received the Nobel Prize in Chemistry for his work in 1960. It 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 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
context_section_description: Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. In photosynthetic pathways ¹²
  C is absorbed slightly more easily than ¹³
  C, which in turn is more easily absorbed than ¹⁴
  C. The differential uptake of the three carbon isotopes leads to ¹³
  C/¹²
  C and ¹⁴
  C/¹²
  C ratios in plants that differ from the ratios in the atmosphere. This effect is known as isotopic fractionation.
  To determine the degree of fractionation that takes place in a given plant, the amounts of both ¹²
  C and ¹³
  C isotopes are measured, and the resulting ¹³
  C/¹²
  C ratio is then compared to a standard ratio known as PDB. The ¹³
  C/¹²
  C ratio is used instead of ¹⁴
  C/¹²
  C because the former is much easier to measure, and the latter can be easily derived: the depletion of ¹³
  C relative to ¹²
  C is proportional to the difference in the atomic masses of the two isotopes, so the depletion for ¹⁴
  C is twice the depletion of ¹³
  C. The fractionation of ¹³
  C, known as δ¹³C, is calculated as follows:
   ‰
  where the ‰ sign indicates parts per thousand. Because the PDB standard contains an unusually high proportion of ¹³
  C, most measured δ¹³C values are negative.
  For marine organisms, the details of the photosynthesis reactions are less well understood, and the δ¹³C values for marine photosynthetic organisms are dependent on temperature. 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 is reduced, and at temperatures above 14 °C the δ¹³C values are correspondingly higher, while at lower temperatures, CO
  ₂ becomes more soluble and hence more available to marine organisms. The δ¹³C value for animals depends on their diet. An animal that eats food with high δ¹³C values will have a higher δ¹³C than one that eats food with lower δ¹³C 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 ¹³
  C than is found in the animal's diet, though for different biochemical reasons. The enrichment of bone ¹³
  C also implies that excreted material is depleted in ¹³
  C relative to the diet.
  Since ¹³
  C makes up about 1% of the carbon in a sample, the ¹³
  C/¹²
  C ratio can be accurately measured by mass spectrometry. Typical values of δ¹³C have been found by experiment for many plants, as well as for different parts of animals such as bone collagen, but when dating a given sample it is better to determine the δ¹³C value for that sample directly than to rely on the published values.
  The carbon exchange between atmospheric CO
  ₂ and carbonate at the ocean surface is also subject to fractionation, with ¹⁴
  C in the atmosphere more likely than ¹²
  C to dissolve in the ocean. The result is an overall increase in the ¹⁴
  C/¹²
  C ratio in the ocean of 1.5%, relative to the ¹⁴
  C/¹²
  C ratio in the atmosphere. This increase in ¹⁴
  C concentration almost exactly cancels out the decrease caused by the upwelling of water (containing old, and hence ¹⁴
  C depleted, carbon) from the deep ocean, so that direct measurements of ¹⁴
  C 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.
caption: North Ronaldsay sheep on the beach in North Ronaldsay. In the winter, these sheep eat seaweed, which has a higher δ13C content than grass; samples from these sheep have a δ13C value of about −13‰, which is much higher than for sheep that feed on grasses.[44]
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