Bohr magneton

Take the orbital current of an electron in Bohr's 1913 atom and you get a magnetic moment of eħ/2mₑ. Every atomic magnetic moment is quoted as a multiple of it, and because the electron's spin g-factor is almost exactly 2, a single unpaired electron spin carries very nearly one Bohr magneton. That is the entire arithmetic of paramagnetism: count unpaired electrons, multiply by μ_B, and you predict how hard a substance is pulled into a field.

In an applied field B the two spin states of a free electron split in energy by 2μ_B·B, which is 1.16 K per tesla in temperature units and 28 GHz per tesla in frequency — the working equation of electron spin resonance. Stern and Gerlach saw the splitting directly in 1922 by firing silver atoms through an inhomogeneous magnet and finding two spots on the glass instead of a smear, the first hard evidence that angular momentum is quantised.