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NMR stands for nuclear magnetic resonance and it is a spectroscopic technique that is commonly used among chemists for identifying chemical structures. A small sample of a chemical is subjected to a powerful magnetic field. This causes the particular atoms being probed (most commonly hydrogens or carbons) to orient themselves with the field. The atoms can spin in two different directions within the field and there is an energy difference between these two spin states. When the sample is exposed to a spectrum of external radiation, the atoms flip their spin depending on when energy of the radiation matches the energy difference between the spin states. This information is then converted to a line spectrum. When probing for any atom, neighboring atoms of the same element will affect the spin flip energy of each of the atoms and result in a splitting pattern for their peaks in the spectrum. This is called coupling and the measured distances between the splitting in the peaks are called the coupling constants. This is very useful for basic proton NMR to determine the chemical structure. This is not very useful for carbon NMR since the splitting patterns get very complex due to the fact that carbon is the most common element present in most organic molecules. So carbon NMR is run with a decoupler which negates this carbon-carbon coupling and produces only singlets in the spectrum. You can run a carbon NMR without the decoupling but as I said before the patterns get very complex and are not generally useful.
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