In the above, the mathematics and chemistry have been simplified, however it can be used effectively to give the number of carbon atoms for small- to medium-sized organic molecules.
Due to differential uptake in plants as well as marine carbonates of 13C, it is possible to use these isotopic signatures in earth science.
[2] Tree ring analysis of carbon isotopes can be used to retrospectively understand forest photosynthesis and how it is impacted by drought.
Carbon-13 has a non-zero spin quantum number of 1/2, and hence allows the structure of carbon-containing substances to be investigated using carbon-13 nuclear magnetic resonance.
The carbon-13 urea breath test is a safe and highly accurate diagnostic tool to detect the presence of Helicobacter pylori infection in the stomach.
[5] Industrial carbon-13 production plants represent a substantial investment, greater than 100 meter tall cryogenic distillation columns are needed to separate the carbon-12 or carbon-13 containing compounds.
[7] In contrast, a 1969 carbon monoxide cryogenic distillation pilot plant at Los Alamos Scientific Laboratories could produce 4 kg of carbon-13 annually.