page_title: Radiocarbon dating considerations
section_title: Isotopic fractionation
hierarchical_section_title: Radiocarbon 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: The variation in the ¹⁴
  C/¹²
  C ratio in different parts of the carbon exchange reservoir means that a straightforward calculation of the age of a sample based on the amount of ¹⁴
  C it contains will often give an incorrect result. There are several other possible sources of error that need to be considered. The errors are of four general types:
  Variations in the ¹⁴
  C/¹²
  C ratio in the atmosphere, both geographically and over time
  Isotopic fractionation
  Variations in the ¹⁴
  C/¹²
  C ratio in different parts of the reservoir
  Contamination
context_section_description: Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. Two different photosynthetic processes exist: the C3 pathway and the C4 pathway. About 90% of all plant life uses the C3 process; the remaining plants either use C4 or are CAM plants, which can use either C3 or C4 depending on the environmental conditions. Both the C3 and C4 photosynthesis pathways show a preference for lighter carbon, with ¹²
  C being 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 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 because it is much easier to measure than the ¹⁴
  C/¹²
  C ratio, and the ¹⁴
  C/¹²
  C ratio can be easily derived from it.)  The resulting value, known as δ¹³C, is calculated as follows:
   ‰
  where the ‰ (permil) sign indicates parts per thousand.  Because the PDB standard contains an unusually high proportion of ¹³
  C, most measured δ¹³C values are negative. Values for C3 plants typically range from −30‰ to −22‰, with an average of −27‰; for C4 plants the range is −15‰ to −9‰, and the average is −13‰. Atmospheric CO
  ₂ has a δ¹³C of −8‰.
  For marine organisms, the details of the photosynthesis reactions are less well understood. Measured δ¹³C values for marine plankton range from −31‰ to −10‰; most lie between −22‰ and −17‰. The δ¹³C values for marine photosynthetic organisms also depend 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, reaching −13‰. At lower temperatures, CO
  ₂ becomes more soluble and hence more available to the marine organisms; fractionation increases and δ¹³C values can be as low as −32‰.
  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 affect 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 depletion of ¹³
  C relative to ¹²
  C is proportional to the difference in the atomic masses of the two isotopes, so once the δ¹³C value is known, the depletion for ¹⁴
  C can be calculated: it will be twice the depletion of ¹³
  C.
  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 differen
caption: 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.[9]
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