carbon-14

Examples of carbon-14 in the following topics:

• Half-Life and Rate of Decay; Carbon-14 Dating

  • Carbon-14 dating is a radiometric dating method that uses the radioisotope carbon-14 (14C) to estimate the age of object.
  • There are also trace amounts of the unstable radioisotope carbon-14 (14C) on Earth.
  • Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.
  • Both processes of formation and decay of carbon-14 are shown in .
  • Diagram of the formation of carbon-14 (1), the decay of carbon-14 (2), and equations describing the carbon-12:carbon-14 ratio in living and dead organisms

• Practice 2: Exponential Distribution

  • Carbon-14 is a radioactive element with a half-life of about 5730 years.
  • Carbon-14 is said to decay exponentially.
  • We start with 1 gram of carbon-14.
  • We are interested in the time (years) it takes to decay carbon-14.
  • Exercise 5.7.7: Find the percentage of carbon-14 lasting longer than 10,000 years.

• Isotopes

  • Carbon-14 (or 14C) contains six protons, eight neutrons, and six electrons; its atomic mass is 14 amu (six protons and eight neutrons).
  • Carbon-12 (12C) is the most abundant of the carbon isotopes, accounting for 98.89% of carbon on Earth.
  • Carbon-14 (14C) is unstable and only occurs in trace amounts.
  • Carbon is normally present in the atmosphere in the form of gaseous compounds like carbon dioxide and methane.
  • Carbon-14 (14C) is a naturally-occurring radioisotope that is created from atmospheric 14N (nitrogen) by the addition of a neutron and the loss of a proton, which is caused by cosmic rays.

• Carbon Dating and Estimating Fossil Age

  • Beds that preserve fossils typically lack the radioactive elements needed for radiometric dating ("radiocarbon dating" or simply "carbon dating").
  • The half-life of carbon-14 is 5,730 years, so carbon dating is only relevant for dating fossils less than 60,000 years old.
  • Carbon dating uses the decay of carbon-14 to estimate the age of organic materials, such as wood and leather.
  • Radiometric dating is a technique used to date materials such as rocks or carbon, usually based on a comparison between the observed abundance of a naturally occurring radioactive isotope and its decay products, using known decay rates.

• Analysis of Molecular Formulas

  • The number of hydrogen atoms that can be bonded to a given number of carbon atoms is limited by the valence of carbon.
  • For compounds of carbon and hydrogen (hydrocarbons) the maximum number of hydrogen atoms that can be bonded to n carbons is 2n + 2 (n is an integer).
  • Here the middle carbons will each have two hydrogens and the two end carbons have three hydrogens each.
  • Thus, a six-carbon chain (n = 6) may be written H-(CH2)6-H, and the total hydrogen count is (2 x 6) + 2 = 14.
  • If the four carbon atoms form a ring, two hydrogens must be lost.

• Properties of Carbon

  • As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds.
  • Allotropes of carbon are not limited to diamond and graphite, but also include buckyballs (fullerenes), amorphous carbon, glassy carbon, carbon nanofoam, nanotubes, and others.
  • Carbon has two stable, naturally occurring isotopes: carbon-12 and carbon-13.
  • Carbon-12 makes 98.93% and carbon-13 forms the remaining 1.07%.
  • Some allotropes of carbon: a) diamond, b) graphite, c) lonsdaleite, d–f) fullerenes (C60, C540, C70); g) amorphous carbon, h) carbon nanotube.

• Naming Aromatic Compounds

  • Aromatic compounds are ring structures with unusual stability due to delocalized pi electron density that is shared between all of the carbon atoms in the ring.
  • Alkyl groups are named according to the alkane series convention ending with -yl: methyl (for a single carbon), ethyl (for two carbons), propyl (for three carbons), etc.
  • If the substituent contains more than six carbons, the alkane portion is named first, and the aromatic ring portion is added as a suffix.
  • For instance, an aromatic ring bonded to an 8-carbon chain would be 1-phenyloctane, and not octylbenzene.
  • Disubstituted benzene rings can be named based on the relative positions of the substituents: the prefix ortho- is used if the substituents occupy adjacent positions on the ring (1,2), meta- is used if the substituents are separated by one ring position (1,3), and para- if they are found on opposite sides of the ring (1,4).

• Diastereoselection in Reactions with Chiral Enolates

  • The two equations in the following diagram show examples in which 1,4-diastereoselection (red asterisks) might result from such an aldol reaction involving enolate derivatives of a methyl ketone.
  • Example 4 demonstrates the exceptional 1,2- and 1,4-diastereoselectivity that can be achieved with both enolborinates and chlorotitanium enolates.
  • However, the 1,4-diastereoselectivity (α':β) is not consistent.
  • The 1,4-anti-selectivity shown in reactions 6 and 7 is predicted by the transition state model, but the 1,4-syn-selectivity and 1,3-anti selectivity (α':α) in reaction 5 is anomalous.
  • A final example of the remarkable directive influence that neighboring chiral centers may exert on carbon-carbon bond forming reactions is found in the 1,5-diastereoselectivity induced by β-substituents present in methyl ketone donors.

• Polar Functions and Umpolung

  • In the above list of classic reactions for carbon-carbon bond formation we find many applications involving polar functional groups, such as the carbonyl group.
  • In these cases it is useful to consider the event as a bond formation between a carbon electrophile and a carbon nucleophile, as shown below.
  • As shown in the following diagram, the carbon-halogen bond is dipolar, with the carbon being positive (electrophilic) and the halogen negative.
  • This intermediate also adds in a conjugate fashion to activated alkenes, such as acrylonitrile and methyl vinyl ketone, producing β-ketonitriles and 1,4-diketones.
  • Since the benzoin condensation is reversible, the 1,4-addition product is favored.

• Reactions of Simple Organometallic Compounds

  • The ionic character of the carbon-mercury bond is estimated to be less than 10%.
  • Ketones and esters react to give 3º-alcohols (examples 12 & 14).
  • The examples in group VI illustrate addition reactions to epoxides, carbon dioxide and carbon double bonds activated by conjugation with carbonyl groups.
  • Nucleophilic addition reactions to α,β-unsaturated ketones may take place in two ways: 1,2-addition to the carbonyl function, or 1,4-conjugate addition to the enone.
  • Simple alkyllithium reagents usually add in the 1,2-fashion, but the presence of cuprous salts or the use of Gilman's reagent directs addition in the 1,4-fashion (examples 20 & 21).