Just discovered that I never responded to this! So sorry!
Yes, C13 is an isotope that occurs naturally in all carbon compounds, but at a very low percentage… In a strong magnetic field, all the neutrons “feel” the field, as attenuated by the electrons zipping around them, and when a strong radio frequency is pumped in, while everybody is excited, that “extra” neutron (C12 is the predominant isotope) flips its spin. When it relaxes back to normal, it releases that energy, which is detected as a peak on a graph in ppm relative to the signal of TMS (tetramethylsilane). That “distance” from the resonance of TMS tells us something about the electronic environment of that particular carbon atom, which then leads us to understand the configuration (shape) of the molecule that C13 atom is in. So by adding different heteroatoms to a six-membered ring (say, replace a carbon in cyclohexane with an oxygen atom), all the carbon atoms will now have a different resonance. It’s that difference that gives us a ton of information about molecular shape, and so much more. Back in the day, it was these early studies of carbon and hydrogen magnetic resonance that ultimately led to the non-invasive MRI images we can get today, inside the body! When I was in grad school, the “bore size” was about the diameter of a test tube. It was an immense breakthrough when the physicists and engineers were able to create a stable magnetic field large enough in diameter to put a human inside of! But to answer your other question about dating artifacts, I believe it’s the C14 isotope that’s used. It’s radioactive and decays over long periods of time, allowing “dating”…
And so much more. I hope this whets, rather than quenches, your appetite for more… I love this subject. I got so deeply intimate with subatomic particles that they began to have personalities, likes, and dislikes. I even named a few. But that was then. Now, after being a professor of organic chem, and moving on to the department of defense, and later an entrepreneur (I invented a “cure” for mange and yeast infections in animals), I’m so totally retired and lazy… but still fascinated by what goes on deep deep deep down where mysteries abound… :D
