A note on the gyromagnetic properties of the hydrogens

How do NMR experiments work? This question is addressed at the undergraduate level in both chemistry and physics lectures and laboratories. In most descriptions,¹ it is taken for granted (without discussion) that hydrogen NMR is proton NMR and how, for hydrogen, an external magnetic field creates a two-state quantum system with an energy gap simply and directly proportional to the value of the nuclear magnetic moment. No mention is made of the magnetic moment of the two electrons that make up the covalent bond connecting the hydrogen atom to the (most often) carbon backbone of the molecule. Nor is any mention made of the complete cancellation of the electron-induced magnetic field at the hydrogen nucleus; that is, the cancellation of the hyperfine splitting (HFS) that is necessary for this technique to yield such simple data. The chemist will examine this point and say that the paired electrons are diamagnetic...