Isotopes of carbon

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Carbon (₆C) has 14 known isotopes, from ⁸
C
to ²⁰
C
as well as ²²
C
, of which ¹²
C
and ¹³
C
are stable. The longest-lived radioisotope is ¹⁴
C
, with a half-life of 5.70(3)×10³ years. This is also the only carbon radioisotope found in nature, as trace quantities are formed cosmogenically by the reaction ¹⁴
N
+
n
→ ¹⁴
C
+ ¹
H
. The most stable artificial radioisotope is ¹¹
C
, which has a half-life of 20.3402(53) min. All other radioisotopes have half-lives under 20 seconds, most less than 200 milliseconds. The least stable isotope is ⁸
C
, with a half-life of 3.5(1.4)×10⁻²¹ s. Light isotopes tend to decay into isotopes of boron and heavy ones tend to decay into isotopes of nitrogen.

Carbon-11 or ¹¹
C
is a radioactive isotope of carbon that decays to boron-11. This decay mainly occurs due to positron emission, with around 0.19–0.23% of decays instead occurring by electron capture.^[6][7] It has a half-life of 20.3402(53) min.

¹¹
C
→ ¹¹
B
+
e⁺
+
ν
_e + 0.96 MeV

¹¹
C
+
e⁻
→ ¹¹
B
+
ν
_e + 1.98 MeV

It is produced by hitting nitrogen with protons of around 16.5 MeV in a cyclotron. The causes the endothermic reaction^[8][9]

¹⁴
N
+
p
→ ¹¹
C
+ ⁴
He
− 2.92 MeV

It can also be produced by fragmentation of ¹²
C
by shooting high-energy ¹²
C
at a target.^[10]

Carbon-11 is commonly used as a radioisotope for the radioactive labeling of molecules in positron emission tomography. Among the many molecules used in this context are the radioligands [¹¹
C
]DASB and [¹¹
C
]Cimbi-5.

There are three naturally occurring isotopes of carbon: 12, 13, and 14. ¹²
C
and ¹³
C
are stable, occurring in a natural proportion of approximately 93:1. ¹⁴
C
is produced by thermal neutrons from cosmic radiation in the upper atmosphere, and is transported down to earth to be absorbed by living biological material. Isotopically, ¹⁴
C
constitutes a negligible part; but, since it is radioactive with a half-life of 5.70(3)×10³ years, it is radiometrically detectable. Since dead tissue does not absorb ¹⁴
C
, the amount of ¹⁴
C
is one of the methods used within the field of archeology for radiometric dating of biological material.

¹²
C
and ¹³
C
are measured as the isotope ratio δ¹³C in benthic foraminifera and used as a proxy for nutrient cycling and the temperature dependent air–sea exchange of CO₂ (ventilation).^[11] Plants find it easier to use the lighter isotopes (¹²
C
) when they convert sunlight and carbon dioxide into food. For example, large blooms of plankton (free-floating organisms) absorb large amounts of ¹²
C
from the oceans. Originally, the ¹²
C
was mostly incorporated into the seawater from the atmosphere. If the oceans that the plankton live in are stratified (meaning that there are layers of warm water near the top, and colder water deeper down), then the surface water does not mix very much with the deeper waters, so that when the plankton dies, it sinks and takes away ¹²
C
from the surface, leaving the surface layers relatively rich in ¹³
C
. Where cold waters well up from the depths (such as in the North Atlantic), the water carries ¹²
C
back up with it; when the ocean was less stratified than today, there was much more ¹²
C
in the skeletons of surface-dwelling species. Other indicators of past climate include the presence of tropical species and coral growth rings.^[12]

The quantities of the different isotopes can be measured by mass spectrometry and compared to a standard; the result (e.g., the delta of the ¹³
C
= δ¹³
C
) is expressed as parts per thousand (‰) divergence from the ratio of a standard:^[13]

${\displaystyle \delta {\ce {^{13}C}}=\left({\frac {\left({\frac {{\ce {^{13}C}}}{{\ce {^{12}C}}}}\right)_{\text{sample}}}{\left({\frac {{\ce {^{13}C}}}{{\ce {^{12}C}}}}\right)_{\text{standard}}}}-1\right)\times 1000}$ ‰

The usual standard is Peedee Belemnite, abbreviated "PDB", a fossil belemnite. Due to shortage of the original PDB sample, artificial "virtual PDB", or "VPDB", is generally used today.^[14]

Stable carbon isotopes in carbon dioxide are utilized differentially by plants during photosynthesis.^{[citation needed]} Grasses in temperate climates (barley, rice, wheat, rye, and oats, plus sunflower, potato, tomatoes, peanuts, cotton, sugar beet, and most trees and their nuts or fruits, roses, and Kentucky bluegrass) follow a C3 photosynthetic pathway that will yield δ¹³C values averaging about −26.5‰.^{[citation needed]} Grasses in hot arid climates (maize in particular, but also millet, sorghum, sugar cane, and crabgrass) follow a C4 photosynthetic pathway that produces δ¹³C values averaging about −12.5‰.^[15]

It follows that eating these different plants will affect the δ¹³C values in the consumer's body tissues. If an animal (or human) eats only C3 plants, their δ¹³C values will be from −18.5 to −22.0‰ in their bone collagen and −14.5‰ in the hydroxylapatite of their teeth and bones.^[16]

In contrast, C4 feeders will have bone collagen with a value of −7.5‰ and hydroxylapatite value of −0.5‰.

In actual case studies, millet and maize eaters can easily be distinguished from rice and wheat eaters. Studying how these dietary preferences are distributed geographically through time can illuminate migration paths of people and dispersal paths of different agricultural crops. However, human groups have often mixed C3 and C4 plants (northern Chinese historically subsisted on wheat and millet), or mixed plant and animal groups together (for example, southeastern Chinese subsisting on rice and fish).^[17]

• Cosmogenic isotopes
• Environmental isotopes
• Isotopic signature
• Radiocarbon dating