## More Chemistry

15 isotopes of the element carbon are known - 2 of which are stable (^{12}C, ^{13}C), the others occur as unstable natural decomposition products (^{14} C) on or were artificially generated. The carbon radioisotope with the longest half-life (5700 years) is C-14, which also occurs in traces in nature.

Natural carbon is therefore a mixture of C-12 and C-13 as well as traces of C-14 with the following isotopic composition:

Atomic Mass m_{a} | Quantity | Half-life | Spin | |

Carbon Isotopic mixture | 12,011 u | 100 % | ||

Isotope ^{12}C | 12,00000000000 u | 98,94 % | stable | 0+ |

Isotope ^{13}C | 13,003354835(2) u | 1,06 % | stable | 1/2- |

Isotope ^{14}C | 14,003241988(4) u | traces | 5700(30) a | 0+ |

The carbon isotope C-11 is used as a radioisotope in positron emission tomography: [^{11}C]DASB and others.

C-14 - also known as radiocarbon - is the radioactive carbon isotope contained in small traces (1:1 trillion) in natural carbon. It is mainly formed in the atmosphere by the effect of cosmic radiation on ^{14}N nitrogen isotopes by neutron capture and the release of a proton:

^{14}N + ^{1}n rarr; ^{14}C + ^{1}p.

The ^{14} radioisotopes enter the terrestrial carbon cycle - for example as ^{14}CO_{2} and are distributed widely and evenly, especially in living organisms. Overall, there is a balance between "normal", stable carbon and radiocarbon. The ^{14}C nuclides, which decay with a half-life of 5700 years, are constantly being replenished from the atmosphere as long as there is a possibility of exchange between air and matter; overall there is a fairly constant equilibrium - a so-called dynamic equilibrium between decay and formation - ^{12/13}C to ^{14}C of 1 : 10^{12}.

The radiocarbon atoms gradually decay back to nitrogen-14, releasing an electron (β^{-} radiation) and a neutrino *v*:

^{14}C → ^{14}N + e^{-} + *v*.

This balance of the carbon isotopes in other organic carbon-containing materials forms the basis for a method for determining the age, which is known under the names C14 analysis, ^{14}C dating, radiocarbon dating or radiocarbon method or radiocarbon dating Radiocarbon dating is known: After an organism dies, the C14 atoms decay as described. If the dead parts do not get back into the natural cycle (e.g. wood, bones, etc.) or only slowly, then the C14 content will continue to decrease over time. By determining the proportion of ^{14}C and corresponding conversions, the age of a given sample can be determined within a time frame of around 300 to 60,000 years.

Isotope Nuclide | E | N | Atomic Mass [Nuclear Mass] {Mass Excess} | Spin I(h/2π) | Parent |
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 |

Carbon-8 | 86C | 2 | 8.037643(20) u [8.0343515 u] {35.06423 MeV} | 0+ | |

Carbon-9 | 96C | 3 | 9.0310372(23) u [9.0277457 u] {28.91097 MeV} | (3/2-) | |

Carbon-10 | 106C | 4 | 10.01685322(7) u [10.0135618 u] {15.69867 MeV} | 0+ | |

Carbon-11 | 116C | 5 | 11.01143260(6) u [11.0081411 u] {10.6494 MeV} | 3/2- | |

Carbon-12 | 126C | 6 | 12.00000000000 u [11.9967085 u] {0 MeV} | 0+ | ^{12}B^{12}N |

Carbon-13 | 136C | 7 | 13.003354835(2) u [13.0000634 u] {3.12501 MeV} | 1/2- | ^{13}B^{13}N |

Carbon-14 | 146C | 8 | 14.003241988(4) u [13.9999505 u] {3.01989 MeV} | 0+ | ^{14}B |

Carbon-15 | 156C | 9 | 15.0105993(9) u [15.0073078 u] {9.87318 MeV} | 1/2+ | |

Carbon-16 | 166C | 10 | 16.014701(4) u [16.0114095 u] {13.69389 MeV} | 0+ | |

Carbon-17 | 176C | 11 | 17.022579(19) u [17.0192875 u] {21.0322 MeV} | 3/2+ | |

Carbon-18 | 186C | 12 | 18.02675(3) u [18.0234585 u] {24.91746 MeV} | 0+ | |

Carbon-19 | 196C | 13 | 19.03480(11) u [19.0315085 u] {32.41599 MeV} | (1/2+) | |

Carbon-20 | 206C | 14 | 20.04026(25) u [20.0369685 u] {37.50195 MeV} | 0+ | |

Carbon-21 | 216C | 15 | 21.04900(64) u [21.0457085 u] {45.64321 MeV} | (1/2+) | |

Carbon-22 | 226C | 16 | 22.05755(25) u [22.0526785 u] {52.13572 MeV} | 0+ |

Isotope | Radioactive Decay | Extern | |||
---|---|---|---|---|---|

Half-life | Decay Mode | Probability | Energy | ||

7 | 8 | 9 | 10 | 11 | 12 |

C-8 | 2.86 × 10^{-21} s | 2p → ^{6}Be | 12.143 MeV | AL | |

C-9 | 126.5(9) ms | β^{+}, p → ^{8}Beβ ^{+}, α → ^{5}Li | 61.6 % 38.4 % | 16.4945 MeV | AL |

C-10 | 19.290(12) s | β^{+} → ^{10}B | 3.64806(7) MeV | AL | |

C-11 | 20.364(14) min | β^{+} → ^{11}BEC → ^{11}B | 99.79 % 0.21 % | 1.98169(6) MeV 0.96 MeV | AL |

C-12 | stable | AL | |||

C-13 | stable | AL | |||

C-14 | 5700(30) a | β^{-} → ^{14}N | 100 % | 0.156476(4) MeV | AL |

C-15 | 2.449(5) s | β^{-} → ^{15}N | 100 % | 9.7717(8) MeV | AL |

C-16 | 747(8) s | β^{-} → ^{16}Nβ ^{-}, n → ^{15}N | 2.1 % 97.9 % | 8.010 MeV 5.521 MeV | AL |

C-17 | 193(6) ms | β^{-} → ^{17}Nβ ^{-}, n → ^{16}N | 71.6 % 28.4 % | 13.162 MeV 7.277 MeV | AL |

C-18 | 92(2) ms | β^{-} → ^{18}Nβ ^{-}, n → ^{17}N | 68.5 % 31.5(5) % | 11.810 MeV 8.980 MeV | AL |

C-19 | 46.3(40) ms | β^{-}, n → ^{18}Nβ ^{-} → ^{19}Nβ ^{-}, 2n → ^{17}N | 47.0 % 46.0 % 7 % | AL | |

C-20 | 16.3 ms | β^{-} → ^{20}Nβ ^{-}, n → ^{19}Nβ ^{-}, 2n → ^{18}Nβ ^{-}, 3n → ^{17}N | 100 % 65(18) % < 18.6 % ? | AL | |

C-21 | < 30 ns | n → ^{20}C | AL | ||

C-22 | 6.1 ms | β^{-} → ^{22}Nβ ^{-}, n → ^{21}Nβ ^{-}, 2n → ^{20}N | AL |

Notes (related to the columns):

1 - name of the nuclide, isotope.

2 - E: isotope symbol with mass number (superscript; number of nucleons) and atomic number (subscript; number of protons).

3 - *N*: number of neutrons.

4 - relative atomic mass of the Carbon isotope (isotopic mass including electrons) and the mass of the atomic nucleus in square brackets (nuclear mass, nuclide mass without electrons), each related to ^{12}C = 12.00000 [2]. In addition, the mass excess is given in MeV.

5 - nuclear spin *I*, unit: h/2π.

6 - source nuclides: Possible, assumed or actual source nuclides (mother nuclides, parent nuclides). If applicable, the corresponding decay modes can be found in the data for the respective starting nuclide.

7 - isotope notation in short form.

8 - decay: half-live of the Carbon isotope (a = years; ; d = days; h = hours; min = minutes; s = seconds).

9 - decay mode: type of decay into the respective daughter nuclides with n = neutron emission; p = proton emission; α = alpha decay; β^{-} = beta minus decay with electron emission; EC = electron capture; β^{+} = positron emission; ε = β^{+} and/or EC; Iso = isomeric transition; CD = cluster decay; SF = spontaneous decay.

10 - decay probability in percent (%).

11 - decay energy; Particle energy related to decay type.

12 - other information and notes: AL = Adopted Levels (link to external data [1]).

Miscellaneous:

()- Numbers in brackets: uncertainty to represent the spread of the reported value.

~ - Theoretical values or systematic trends.

- unlisted-: Nuclides that have already been mentioned in the literature but for some reason can no longer be found in the current nuclide tables because their discovery e.g. has not confirmed.

Nuclide quantity ^{1})spin | Nuclear magnetic moment μ/μ _{N} | Gyromagnetic ratio {Quadrupole moment} | Resonant frequency v_{0} bei 1 T | Relative sensitivity H_{0} = const.v_{0} = const. ^{3}) |
---|---|---|---|---|

^{13}C1,06 % 1/2- | + 0,702369(4) | 6,7283 {} | 10,7084 | 0,01591 0,2515 |

^{1}) Quantity Percentage of natural occurrence.

^{2}) Gyromagnetic ratio: 10^{7} rad T^{-1} s^{-1}

Quadrupole moment: Q fm^{-2}

^{3}) Related to ^{1}H = 1,000.

According to the Radiation Protection Ordinance (StrlSchV 2018, Germany), the following values (columns 1 to 7) apply to the handling of Carbon radionuclides:

Nuclide | Limit Value | HASS limit | SC | Daughter Nuclides | Half-life | |
---|---|---|---|---|---|---|

C-11 | 10^{6} Bq | 10 Bq/g | 0,06 TBq | 20.4 min | ||

C-14 | 10^{7} Bq | 1 Bq/g | 50 TBq | 100 Bq/cm^{2} | 5700 a |

(HASS = High-Activity Sealed Radioactive Sources; SC = surface contamination)

**Properties of the Carbon nucleides**

[1] - NuDat: National Nuclear Data Center, Brookhaven National Laboratory, based on ENSDF and the Nuclear Wallet Cards.

[2] - G. Audi et. al.: The NUBASE evaluation of nuclear and decay properties. Nuclear Physics, (2003), DOI 10.1016/j.nuclphysa.2003.11.001.

[3] - Live Chart of Nuclides. Nuclear structure and decay data.

**Carbon: NMR properties - ^{13}C-NMR **

[4] - N. J. Stone: Table of nuclear magnetic dipole and electric quadrupole moments. Atomic Data and Nuclear Data Tables, (2005), DOI 10.1016/j.adt.2005.04.001.

[5] - Pekka Pyykkö: Year-2008 nuclear quadrupole moments. Molecular Physics, (2008), DOI 10.1080/00268970802018367.

[6] - Pekka Pyykkö: Year-2017 nuclear quadrupole moments. Molecular Physics, (2018), DOI 10.1080/00268976.2018.1426131.

[7] - N. J. Stone: Table of recommended nuclear magnetic dipole moments. IAEA, (2019).

**More sources:**

[8] - **Isotopic abundances, atomic weights and isotopic masses:** see respective keyword.

[9] - NN:**Hoyle-Zustand von Kohlenstoff-12**.

In: Internetchemie News, (2012).

**Last update: **2022-12-12

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