# Isotopes of carbon

Carbon ($_6$C) has 14 known isotopes, from $^8$ C to $^{20}$ C as well as $^{22}$ C , of which only $^{12}$ C and $^{13}$ C are stable. The longest-lived radioisotope is $^{14}$ C , with a half-life of 5.70(3)×10$^3$ 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.

## List of isotopes

| Nuclide | Z | N | Isotopic mass (Da) | Half-life [resonance width] | Decay mode | Daughter isotope | Spin and parity | Natural abundance (mole fraction) | Natural abundance (mole fraction) |
| Nuclide | Z | N | Isotopic mass (Da) | Half-life [resonance width] | Decay mode | Daughter isotope | Spin and parity | Normal proportion | Range of variation |
| $^8$ C | 6 | 2 | 8.037643(20) | 3.5(1.4) zs [230(50) keV] | 2p | $^6$ Be | 0+ | | |
| $^9$ C | 6 | 3 | 9.0310372(23) | 126.5(9) ms | β$^+$ (54.1(1.7)%) | $^9$ B | 3/2− | | |
| $^9$ C | 6 | 3 | 9.0310372(23) | 126.5(9) ms | β$^+$α (38.4(1.6)%) | $^5$ Li | 3/2− | | |
| $^9$ C | 6 | 3 | 9.0310372(23) | 126.5(9) ms | β$^+$p (7.5(6)%) | $^8$ Be | 3/2− | | |
| $^{10}$ C | 6 | 4 | 10.01685322(8) | 19.3011(15) s | β$^+$ | $^{10}$ B | 0+ | | |
| $^{11}$ C | 6 | 5 | 11.01143260(6) | 20.3402(53) min | β$^+$ | $^{11}$ B | 3/2− | | |
| $^{11m}$ C | 12160(40) keV | 12160(40) keV | 12160(40) keV | | p ? | $^{10}$ B ? | 1/2+ | | |
| $^{12}$ C | 6 | 6 | 12 exactly | Stable | Stable | Stable | 0+ | [0.9884, 0.9904] |
| $^{13}$ C | 6 | 7 | 13.003354835336(252) | Stable | Stable | Stable | 1/2− | [0.0096, 0.0116] |
| $^{14}$ C | 6 | 8 | 14.003241989(4) | 5.70(3)×10$^3$ y | β$^−$ | $^{14}$ N | 0+ | Trace | < 10$^{−12}$ |
| $^{14m}$ C | 22100(100) keV | 22100(100) keV | 22100(100) keV | | IT | $^{14}$ C | (2−) | | |
| $^{15}$ C | 6 | 9 | 15.0105993(9) | 2.449(5) s | β$^−$ | $^{15}$ N | 1/2+ | | |
| $^{16}$ C | 6 | 10 | 16.014701(4) | 750(6) ms | β$^−$n (99.0(3)%) | $^{15}$ N | 0+ | | |
| $^{16}$ C | 6 | 10 | 16.014701(4) | 750(6) ms | β$^−$ (1.0(3)%) | $^{16}$ N | 0+ | | |
| $^{17}$ C | 6 | 11 | 17.022579(19) | 193(6) ms | β$^−$ (71.6(1.3)%) | $^{17}$ N | 3/2+ | | |
| $^{17}$ C | 6 | 11 | 17.022579(19) | 193(6) ms | β$^−$n (28.4(1.3)%) | $^{16}$ N | 3/2+ | | |
| $^{17}$ C | 6 | 11 | 17.022579(19) | 193(6) ms | β$^−$2n ? | $^{15}$ N ? | 3/2+ | | |
| $^{18}$ C | 6 | 12 | 18.02675(3) | 92(2) ms | β$^−$ (68.5(1.5)%) | $^{18}$ N | 0+ | | |
| $^{18}$ C | 6 | 12 | 18.02675(3) | 92(2) ms | β$^−$n (31.5(1.5)%) | $^{17}$ N | 0+ | | |
| $^{18}$ C | 6 | 12 | 18.02675(3) | 92(2) ms | β$^−$2n ? | $^{16}$ N ? | 0+ | | |
| $^{19}$ C | 6 | 13 | 19.03480(11) | 46.2(2.3) ms | β$^−$n (47(3)%) | $^{18}$ N | 1/2+ | | |
| $^{19}$ C | 6 | 13 | 19.03480(11) | 46.2(2.3) ms | β$^−$ (46.0(4.2)%) | $^{19}$ N | 1/2+ | | |
| $^{19}$ C | 6 | 13 | 19.03480(11) | 46.2(2.3) ms | β$^−$2n (7(3)%) | $^{17}$ N | 1/2+ | | |
| $^{20}$ C | 6 | 14 | 20.04026(25) | 16(3) ms | β$^−$n (70(11)%) | $^{19}$ N | 0+ | | |
| $^{20}$ C | 6 | 14 | 20.04026(25) | 16(3) ms | β$^−$2n (< 18.6%) | $^{18}$ N | 0+ | | |
| $^{20}$ C | 6 | 14 | 20.04026(25) | 16(3) ms | β$^−$ (> 11.4%) | $^{20}$ N | 0+ | | |
| $^{22}$ C | 6 | 16 | 22.05755(25) | 6.2(1.3) ms | β$^−$n (61(14)%) | $^{21}$ N | 0+ | | |
| $^{22}$ C | 6 | 16 | 22.05755(25) | 6.2(1.3) ms | β$^−$2n (< 37%) | $^{20}$ N | 0+ | | |
| $^{22}$ C | 6 | 16 | 22.05755(25) | 6.2(1.3) ms | β$^−$ (> 2%) | $^{22}$ N | 0+ | | |
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* ↑ ( ) – Uncertainty (1σ) is given in concise form in parentheses after the corresponding last digits.
* ↑ Modes of decay: EC:Electron capture n:Neutron emission p:Proton emission
* ↑ Bold symbol as daughter – Daughter product is stable.
* ↑ ( ) spin value – Indicates spin with weak assignment arguments.
* ↑ # – Values marked # are not purely derived from experimental data, but at least partly from trends of neighboring nuclides (TNN).
* ↑ Subsequently decays by double proton emission to $^4$ He for a net reaction of $^8$ C → $^4$ He + 4$^1$ H
* ↑ Immediately decays by proton emission to $^4$ He for a net reaction of $^9$ C → 2 $^4$ He + $^1$ H + e$^+$
* ↑ Immediately decays into two $^4$ He atoms for a net reaction of $^9$ C → 2 $^4$ He + $^1$ H + e$^+$
* ↑ Used for labeling molecules in PET scans
* 1 2 3 Decay mode shown is energetically allowed, but has not been experimentally observed to occur in this nuclide.
* ↑ The unified atomic mass unit is defined as 1/12 of the mass of an unbound atom of carbon-12 in its ground state.
* ↑ Ratio of $^{12}$C to $^{13}$C used to measure biological productivity in ancient times and differing types of photosynthesis
* ↑ Has an important use in radiodating (see carbon dating)
* ↑ Primarily cosmogenic, produced by neutrons striking atoms of $^{14}$ N ($^{14}$ N + n → $^{14}$ C + $^1$ H )
* ↑ Has 1 halo neutron
* ↑ Has 2 halo neutrons

## Carbon-11

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. 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
    $^{14}$ 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.
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.

## Natural isotopes

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)×10$^3$ 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.

## Paleoclimate

$^{12}$ C and $^{13}$ C are measured as the isotope ratio δ$^{13}$C in benthic foraminifera and used as a proxy for nutrient cycling and the temperature dependent air–sea exchange of CO$_2$ (ventilation). 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.

## Tracing food sources and diets

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 = δ$^{13}$ C ) is expressed as parts per thousand (‰) divergence from the ratio of a standard:
    $\delta {\ce {^{13}C}}=\left({\frac {\left({\frac {{\ce {^{13}C}}}{{\ce {^{12}C}}}}\right)_{\text{sample}}}{\left({\frac {{\ce {^{13}C}}}{{\ce {^{12}C}}}}\right)_{\text{standard}}}}-1\right)\times 1000$ ‰
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.
Stable carbon isotopes in carbon dioxide are utilized differentially by plants during photosynthesis. 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 δ$^{13}$C values averaging about −26.5‰. Grasses in hot arid climates (maize in particular, but also millet, sorghum, sugar cane, and crabgrass) follow a C4 photosynthetic pathway that produces δ$^{13}$C values averaging about −12.5‰.
It follows that eating these different plants will affect the δ$^{13}$C values in the consumer's body tissues. If an animal (or human) eats only C3 plants, their δ$^{13}$C values will be from −18.5 to −22.0‰ in their bone collagen and −14.5‰ in the hydroxylapatite of their teeth and bones.
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).