Normal carbon, carbon-12, contains six protons and six neutrons. But some small percentage of carbon was created with an extra neutron, giving it an atomic weight of 13. This is very nearly the same as carbon-12, and there would be no reason to note the difference if it were not for the fact that while most plants prefer carbon-12 over carbon-13, some plants do accept greater amounts of carbon-13 than others. We can look at carbon-13/12 ratios to determine certain things about plant evolution, local climates, and even the diets of modern humans.
Just so that no one is confused, carbon-14 is something completely different; it is created through a different process, and it is radioactive. Carbon-12 and Carbon-13 are stable, meaning that they do not break down over time. Carbon-14 is also much less common; About 1.1% of our atmospheric carbon is carbon-13, while only about 0.0000000001% is carbon-14.
Most plants make compounds containing three carbon atoms; these are called C3 cycle plants. These plants tend not to take in carbon-13. Some plants can make compounds using four carbon atoms; these are called C4 cycle plants, or Hatch-Slack pathway plants (I will refer to them as C4 plants in this writeup). C4 plants do not discriminate as much between carbon-12 and carbon-13.
C4 plants use more energy, but by taking in four carbon dioxide molecules at a time they can effectively slow their photorespiration. Because they don't have to open and close their stomata as often they will loose less water in hot, dry climates. They also concentrate the CO2 molecules more efficiently, which is valuable when CO2 levels are low.
Because C4 plants use more energy, if all else is equal the C3 plants will pull ahead in the evolutionary race. Of course, all things are never equal, so the populations of C4 vs. C3 plants is determined by three major conditions. C4 plants thrive when conditions are hotter, dryer, and when there is less CO2 in the atmosphere. C3 plants thrive when humidity is high, temperatures are temperate, and when there are high CO2 levels in the atmosphere. (Because CO2 is a greenhouse gas these conditions are often correlated.) This is useful information to paleoclimatologists, who can test the organic remains (even if it has been lithified into rock) for carbon-13/12 ratios.
The carbon-13/12 is measured in relation to a standard set down by the International Atomic Energy Agency in Vienna. They took a sample from the Cretaceous period deposit of PeeDee belemnite (limestone) formation in South Carolina, USA. The ratio is figured by this formula:
(C-13/C-12)sampled – (C-13/C-12)standard
——————————–––––––---––––––––----------------------- x 1,000
(C-13/C-12)standard
Pee Dee Belemnite has a 13/12 ratio of 0.0112372; samples with ratios greater than 0.0112372 have positive carbon-13 delta values (d13C), while those with ratios less than 0.0112372 have negative delta values. C3 plants have d13C values between -0.022 and -0.030. Type C4 plants have higher values of d13C, between –0.010 and –0.014. (Current atmospheric d13C is close to -0.06).
In addition to this, carbon-13 travels up the food chain, so that animals that eat C4 plants will also have elevated levels of carbon-13 in their body. We can test the hair of humans, for example, to see what percent of the carbon is carbon-13. A higher percentage implies a diet high in C4 plants. This is particularly interesting because corn (maize) is one of the most widespread of the C4 plants. This lets us track the spread of corn through historical populations. (Well, I think it's interesting, anyway.) Sorghum and sugarcane are also C4 plants.
Because both sugarcane and corn are C4 plants, customs and other regulatory agencies can test claims that products such as fruit juices are 'all natural'. If they have any carbon-13, that tells you that they have in fact been sweetened with high fructose corn syrup or cane sugar.
References:
http://homepage.mac.com/uriarte/carbon13.html
http://en.wikipedia.org/wiki/C4_carbon_fixation
http://en.wikipedia.org/wiki/C3_carbon_fixation
http://www4.nau.edu/cpsil/isotopes.htm
The Omnivore's Dilemma by Michael Pollan
Environmental Isotopes in Hydrogeology By Ian Douglas Clark, Peter Fritz.