Isotopes of carbon

Carbon (C) has 16 known isotopes, from ⁸C to ²³C, 2 of which (¹²C and ¹³C) are stable. The longest-lived radioisotope is ¹⁴C with a half-life of 5,700 years. This is also the only carbon radioisotope found in nature, where trace quantities are formed cosmogenically by the reaction ¹⁴N + ¹n -> ¹⁴C + ¹H. The most stable artificial radioisotope is ¹¹C, with a half-life of 20.334 minutes. All other radioisotopes have half-lives under 20 seconds, most less than 200 milliseconds. The least stable isotope is ⁸C, with a half-life of 2.0 x 10⁻²¹ s. Averaging over natural abundances, the standard atomic mass for Carbon is 12.0107(8) u.

Carbon-11

Carbon-11 or ¹¹C is a radioactive isotope of carbon. It decays about 99% by positron emission to boron-11 and .19-.23% by K-capture also to boron-11.^[1]^[2] It has a half-life of 20.38 minutes.

¹¹
C
→ The element link does not exist. +
e⁺
+
ν
_e + 0.96 MeV

¹¹
C
→ The element link does not exist. +
ν
_e + 3.17 MeV

Carbon-11 is commonly used as a radioisotope to radioactive labeling of molecules in positron emission tomography. Among the many molecules used in this context is the radioligand [¹¹
C
]DASB.

Natural isotopes

There are 3 naturally occurring isotopes of carbon: 12, 13, and 14. ¹²C and ¹³C are stable, occurring in a natural proportion of approximately 99:1. ¹⁴C 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 the ¹⁴C constitutes a negligible part, but since it is radioactive with a half-life of 5700 years, it is radiometrically detectable. Since dead tissue doesn't absorb ¹⁴C, the amount of ¹⁴C is used for radiometric dating of biological material, among others within the field of archeology.

Paleoclimate

¹²C and ¹³C 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) (Lynch-Stieglitz et al., 1995). Plants find it easier to use the lighter isotopes (¹²C) when they convert sunlight and carbon dioxide into food. So, for example, large blooms of plankton (free-floating organisms) absorb large amounts of ¹²C from the oceans. The ¹²C was originally mostly incorporated into the seawater from the atmosphere. If the oceans the plankton live in are stratified (meaning that there are layers of warm water near the top, and colder water deeper down) the surface water does not mix with deeper waters very much, so that when the plankton dies it sinks and takes away ¹²C from the surface, leaving the surface layers relatively rich in ¹³C. Where cold waters well up from the depths (such as in the North Atlantic) it carries ¹²C back up with it. So, when the ocean was less stratified than today, there was much more ¹²C in the skeletons of surface-dwelling species. Other indicators of past climate include the presence of tropical species, coral growths rings, etc.^[3]

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 ¹³C = δ¹³C) is expressed as parts per thousand (‰).

\delta ^{13}C={\Biggl (}{\frac {{\bigl (}{\frac {^{13}C}{^{12}C}}{\bigr )}_{sample}}{{\bigl (}{\frac {^{13}C}{^{12}C}}{\bigr )}_{standard}}}-1{\Biggr )}*1000\ ^{o}\!/\!_{oo}

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

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 −12.5‰ in their bone collagen and −14.5‰ in their apatite.^[4]

In contrast, C4 feeders will have bone collagen with a value of −7.5‰ and apatite 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). ^[5]

Table

nuclide symbol	Z(p)	N(n)	isotopic mass (u)	half-life	decay mode(s)^[6]	daughter isotope(s)^{[n 1]}	nuclear spin	representative isotopic composition (mole fraction)	range of natural variation (mole fraction)
⁸C	6	2	8.037675(25)	2.0(4) x 10⁻²¹ s [230(50) keV]	2p	⁶ Be ^{[n 2]}	0+
⁹C	6	3	9.0310367(23)	126.5(9) ms	β⁺ (60%)	⁹ B ^{[n 3]}	(3/2-)
					β⁺, p (23%)	⁸ Be ^{[n 4]}
					β⁺, α (17%)	⁵ Li ^{[n 5]}
¹⁰C	6	4	10.0168532(4)	19.290(12) s	β⁺	¹⁰ B	0+
¹¹C^{[n 6]}	6	5	11.0114336(10)	20.334(24) min	β⁺ (99.79%)	¹¹ B	3/2-
¹¹C^{[n 6]}	6	5	11.0114336(10)	20.334(24) min	K-capture (.21%)^[1]^[2]	¹¹ B	3/2-
¹²C	6	6	12 exactly^{[n 7]}	Stable			0+	0.9893(8)	0.98853-0.99037
¹³C^{[n 8]}	6	7	13.0033548378(10)	Stable			1/2-	0.0107(8)	0.00963-0.01147
¹⁴C^{[n 9]}	6	8	14.003241989(4)	5.70(3) x 10³ years	β⁻	¹⁴ N	0+	Trace^{[n 10]}	<10⁻¹²
¹⁵C	6	9	15.0105993(9)	2.449(5) s	β⁻	¹⁵ N	1/2+
¹⁶C	6	10	16.014701(4)	0.747(8) s	β⁻, n (97.9%)	¹⁵ N	0+
¹⁶C	6	10	16.014701(4)	0.747(8) s	β⁻ (2.1%)	¹⁶ N	0+
¹⁷C	6	11	17.022586(19)	193(5) ms	β⁻ (71.59%)	¹⁷ N	(3/2+)
¹⁷C	6	11	17.022586(19)	193(5) ms	β⁻, n (28.41%)	¹⁶ N	(3/2+)
¹⁸C	6	12	18.02676(3)	92(2) ms	β⁻ (68.5%)	¹⁸ N	0+
¹⁸C	6	12	18.02676(3)	92(2) ms	β⁻, n (31.5%)	¹⁷ N	0+
¹⁹C^{[n 11]}	6	13	19.03481(11)	46.2(23) ms	β⁻, n (47.0%)	¹⁸ N	(1/2+)
					β⁻ (46.0%)	¹⁹ N
					β⁻, 2n (7%)	¹⁷ N
²⁰C	6	14	20.04032(26)	16(3) ms [14(+6-5) ms]	β⁻, n (72.0%)	¹⁹ N	0+
²⁰C	6	14	20.04032(26)	16(3) ms [14(+6-5) ms]	β⁻ (28.0%)	²⁰ N	0+
²¹C	6	15	21.04934(54)#	<30 ns	n	²⁰ C	(1/2+)#
²²C^{[n 12]}	6	16	22.05720(97)#	6.2(13) ms [6.1(+14-12) ms]	β⁻	²² N	0+

^ Bold for stable isotopes
^ Subsequently decays by double proton emission to ⁴He for a net reaction of ⁸C -> ⁴He + 4¹H
^ Immediately decays by proton emission to ⁸Be, which immediately decays to two ⁴He atoms for a net reaction of ⁹C -> 2⁴He + ¹H + e⁺
^ Immediately decays into two ⁴He atoms for a net reaction of ⁹C -> 2⁴He + ¹H + e⁺
^ Immediately decays by proton emission to ⁴He for a net reaction of ⁹C -> 2⁴He + ¹H + e⁺
^ Used for labeling molecules in PET scans
^ The unified atomic mass unit is defined as 1/12 the mass of an unbound atom of Carbon-12 at ground state
^ Ratio of ¹²C to ¹³C 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 ¹⁴N (¹⁴N + ¹n -> ¹⁴C + ¹H)
^ Has 1 halo neutron
^ Has 2 halo neutrons

Notes

The precision of the isotope abundances and atomic mass is limited through variations. The given ranges should be applicable to any normal terrestrial material.
Values marked # are not purely derived from experimental data, but at least partly from systematic trends. Spins with weak assignment arguments are enclosed in parentheses.
Uncertainties are given in concise form in parentheses after the corresponding last digits. Uncertainty values denote one standard deviation, except isotopic composition and standard atomic mass from IUPAC which use expanded uncertainties.
¹²C is of particular importance as it is used as the standard from which atomic masses of all nuclides are measured: its atomic mass is by definition 12.

References

^ ^a ^b Scobie, J. (1 September 1957). "K-capture in carbon 11". Philosophical Magazine. 2 (21): 1089–1099. Bibcode:1957PMag....2.1089S. doi:10.1080/14786435708242737. Retrieved 27 March 2012. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ ^a ^b Campbell, J.L. (NaN undefined NaN). "The ratio of K-capture to positon emission in the decay of 11C". Nuclear Physics A. 96 (2): 279–287. Bibcode:1967NuPhA..96..279C. doi:10.1016/0375-9474(67)90712-9. Retrieved 27 March 2012. {{cite journal}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Tim Flannery The weather makers: the history & future of climate change, The Text Publishing Company, Melbourne, Australia. ISBN 1-920885-84-6
^ Tycot, R.H. (2004) “Stable isotopes and diet: you are what you eat.” Proceedings of the International School of Physics ‘Enrico Fermi’Course CLIV, edited by M. Martini, M. Milazzo and M. Piacentini. Amsterdam: IOS Press.
^ Hedges Richard (2006). "Where does our protein come from?". British Journal of Nutrition. 95: 1031–2.
^ http://www.nucleonica.net/unc.aspx

Isotope masses from:
- G. Audi, A. H. Wapstra, C. Thibault, J. Blachot and O. Bersillon (2003). "The NUBASE evaluation of nuclear and decay properties" (PDF). Nuclear Physics A. 729: 3–128. Bibcode:2003NuPhA.729....3A. doi:10.1016/j.nuclphysa.2003.11.001.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Isotopic compositions and standard atomic masses from:
- J. R. de Laeter, J. K. Böhlke, P. De Bièvre, H. Hidaka, H. S. Peiser, K. J. R. Rosman and P. D. P. Taylor (2003). "Atomic weights of the elements. Review 2000 (IUPAC Technical Report)". Pure and Applied Chemistry. 75 (6): 683–800. doi:10.1351/pac200375060683.{{cite journal}}: CS1 maint: multiple names: authors list (link)
- M. E. Wieser (2006). "Atomic weights of the elements 2005 (IUPAC Technical Report)". Pure and Applied Chemistry. 78 (11): 2051–2066. doi:10.1351/pac200678112051. {{cite journal}}: Unknown parameter |laysummary= ignored (help)
Half-life, spin, and isomer data selected from the following sources. See editing notes on this article's talk page.
- G. Audi, A. H. Wapstra, C. Thibault, J. Blachot and O. Bersillon (2003). "The NUBASE evaluation of nuclear and decay properties" (PDF). Nuclear Physics A. 729: 3–128. Bibcode:2003NuPhA.729....3A. doi:10.1016/j.nuclphysa.2003.11.001.{{cite journal}}: CS1 maint: multiple names: authors list (link)
- National Nuclear Data Center. "NuDat 2.1 database". Brookhaven National Laboratory. Retrieved September 2005. {{cite web}}: Check date values in: |accessdate= (help)
- N. E. Holden (2004). "Table of the Isotopes". In D. R. Lide (ed.). CRC Handbook of Chemistry and Physics (85th ed.). CRC Press. Section 11. ISBN 978-0-8493-0485-9. {{cite book}}: Unknown parameter |nopp= ignored (|no-pp= suggested) (help)