Electronic magnetic dipole intrinsic spin

The electron has a magnetic dipole moment m that stems from its intrinsic an gular moment (spin) hS with ft = hjln, h being the Planck constant. For a free electron m — where = 2.0023 and )8e are the electron Lande -factor... 

This relahon differs in an important way from Equation 10.14. It says that the magnetic dipole moment is proportional to the spin vector with not only a factor of e/2mc but also with an additional factor, g. (Recall at the proportionality factor for orbital angular momentum is e/2mc.) The additional factor is required because the simple picture of circulation of charge that led to Equahon 10.14 does not apply to the intrinsic spin of an electron. The measured value for the dimensionless constant for a free electron is 2.0023. 

Nuclear magnetic resonance (NMR) and electron spin resonance (ESR) provide some of the most powerful and versatile spectroscopic tools of the modem chemist. Each spectroscopy depends on the intrinsic spin angular momentum and associated magnetic dipole moment that is exhibited by nuclei with odd numbers of neutrons or protons, as well as by all electrons. 

The expression for the magnetic dipole moment for the intrinsic spin of an electron is similar to that of an electron in its orbit except that an additional term g, is needed. The additional term is needed because the simple model of a circulating electron used to obtain Equation 8-60 does not apply to the intrinsic spin of an electron. 

Both the orbital motion and the intrinsic spin of electron have a magnetic dipole associated with it. The two magnetic dipoles may interact with one another. This feature of atomic and molecular structure is called spin-orbit interaction. The spin-orbit interaction is a coupling of the two different motions of spin of the electron. The Hamiltonian that describes this interaction is a dot product of the angular momentum vectors of the two different types of spin motions of the electron. The proportionality constant is a which can be measured by spectroscopy. 

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