Editing Radiocarbon dating (section)

===Isotopic fractionation===
{{main|Fractionation of carbon isotopes in oxygenic photosynthesis}}
Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. In photosynthetic pathways {{chem|12|C}} is absorbed slightly more easily than {{chem|13|C}}, which in turn is more easily absorbed than {{chem|14|C}}. The differential uptake of the three carbon isotopes leads to {{chem|13|C}}/{{chem|12|C}} and {{chem|14|C}}/{{chem|12|C}} ratios in plants that differ from the ratios in the atmosphere. This effect is known as isotopic fractionation.<ref name=Bowman_20>Bowman (1995), pp.&nbsp;20–23.</ref><ref name=Leng_246>Maslin & Swann (2006), p.&nbsp;246.</ref>

To determine the degree of fractionation that takes place in a given plant, the amounts of both {{chem|12|C}} and {{chem|13|C}} isotopes are measured, and the resulting {{chem|13|C}}/{{chem|12|C}} ratio is then compared to a [[Reference materials for stable isotope analysis|standard ratio]] known as PDB.{{#tag:ref|"PDB" stands for "Pee Dee Belemnite", a fossil from the [[Pee Dee Formation|Pee Dee formation]] in South Carolina.<ref>Taylor & Bar-Yosef (2014), p. 125.</ref>|group = note}} The {{chem|13|C}}/{{chem|12|C}} ratio is used instead of {{chem|14|C}}/{{chem|12|C}} because the former is much easier to measure, and the latter can be easily derived: the depletion of {{chem|13|C}} relative to {{chem|12|C}} is proportional to the difference in the atomic masses of the two isotopes, so the depletion for {{chem|14|C}} is twice the depletion of {{chem|13|C}}.<ref name=Aitken1990/> The fractionation of {{chem|13|C}}, known as {{delta|13|C|link}}, is calculated as follows:<ref name=Bowman_20/>

:<math chem>\delta \ce{^{13}C} = \left( \frac{\left( \frac{\ce{^{13}C}}{\ce{^{12}C}} \right)_{\text{sample}}}{\left( \frac{\ce{^{13}C}}{\ce{^{12}C}} \right)_{\text{standard}}} - 1 \right) \times 1000</math> ‰

where the ‰ sign indicates [[parts per thousand]].<ref name=Bowman_20/> Because the PDB standard contains an unusually high proportion of {{chem|13|C}},{{#tag:ref|The PDB value is 11.2372‰.<ref>Dass (2007), p. 276.</ref>|group = note}} most measured {{delta|13|C}} values are negative.

[[File:NR sheep.jpg|thumb|upright=1.35|left|[[North Ronaldsay sheep]] on the beach in [[North Ronaldsay]], Scotland. In the winter, these sheep eat seaweed, which has a higher {{delta|13|C}} content than grass; samples from these sheep have a {{delta|13|C}} value of about −13‰, which is much higher than for sheep that feed on grasses.<ref name=Bowman_20/>]]
{| class="wikitable" style="font-size: 10pt; margin-left: 2em; text-align: center; float: right"
! Material !! Typical {{delta|13|C}} range
|-
|PDB || 0‰

|-
| Marine plankton || −22‰ to −17‰<ref name=Leng_246/>
|-
| C3 plants || −30‰ to −22‰<ref name=Leng_246/>
|-
| C4 plants || −15‰ to −9‰<ref name=Leng_246/>
|-
| Atmospheric {{chem|CO|2}} || −8‰<ref name=Bowman_20/>
|-
| Marine {{chem|CO|2}} || −32‰ to −13‰<ref name=Leng_246/>
|}
For marine organisms, the details of the photosynthesis reactions are less well understood, and the {{delta|13|C}} values for marine photosynthetic organisms are dependent on temperature. At higher temperatures, {{chem|CO|2}} has poor solubility in water, which means there is less {{chem|CO|2}} available for the photosynthetic reactions. Under these conditions, fractionation is reduced, and at temperatures above 14&nbsp;°C the {{delta|13|C}} values are correspondingly higher, while at lower temperatures, {{chem|CO|2}} becomes more soluble and hence more available to marine organisms.<ref name=Leng_246/> The {{delta|13|C}} value for animals depends on their diet. An animal that eats food with high {{delta|13|C}} values will have a higher {{delta|13|C}} than one that eats food with lower {{delta|13|C}} values.<ref name=Bowman_20/> 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 {{chem|13|C}} than is found in the animal's diet, though for different biochemical reasons. The enrichment of bone {{chem|13|C}} also implies that excreted material is depleted in {{Chem|13|C}} relative to the diet.<ref>Schoeninger (2010), p. 446.</ref>

Since {{chem|13|C}} makes up about 1% of the carbon in a sample, the {{chem|13|C}}/{{chem|12|C}} ratio can be accurately measured by [[mass spectrometry]].<ref name=Aitken1990/> Typical values of {{delta|13|C}} 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 {{delta|13|C}} value for that sample directly than to rely on the published values.<ref name=Bowman_20/>

The carbon exchange between atmospheric {{chem|CO|2}} and carbonate at the ocean surface is also subject to fractionation, with {{chem|14|C}} in the atmosphere more likely than {{chem|12|C}} to dissolve in the ocean. The result is an overall increase in the {{chem|14|C}}/{{chem|12|C}} ratio in the ocean of 1.5%, relative to the {{chem|14|C}}/{{chem|12|C}} ratio in the atmosphere. This increase in {{chem|14|C}} concentration almost exactly cancels out the decrease caused by the upwelling of water (containing old, and hence {{chem|14|C}}-depleted, carbon) from the deep ocean, so that direct measurements of {{chem|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.<ref name=Aitken1990/><ref name=Cronin2010/>