# electron spin

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## Electron spin

That property of an electron which gives rise to its angular momentum about an axis within the electron. Spin is one of the permanent and basic properties of the electron. Both the spin and the associated magnetic dipole moment of the electron were postulated by G. E. Uhlenbeck and S. Goudsmit in 1925 as necessary to allow the interpretation of many observed effects, among them the so-called anomalous Zeeman effect, the existence of doublets (pairs of closely spaced lines) in the spectra of the alkali atoms, and certain features of x-ray spectra. *See* Spin (quantum mechanics)

The spin quantum number is *s*, which is always ½. This means that the component of spin angular momentum along a preferred direction, such as the direction of a magnetic field, is ±½ℏ, where ℏ = *h*/2&pgr; and *h* is Planck's constant. The spin angular momentum of the electron is not to be confused with the orbital angular momentum of the electron associated with its motion about the nucleus. In the latter case the maximum component of angular momentum along a preferred direction is *l*ℏ, where *l* is the angular momentum quantum number and may be any positive integer or zero. *See* Angular momentum, Quantum numbers

#### Electron magnetic moment

The electron has a magnetic dipole moment by virtue of its spin. The approximate value of the dipole moment is the Bohr magneton μ_{0} which is equal, in SI units, to *e**h*/4&pgr;*m* = 9.27 × 10^{-24} joule/tesla, where *e* is the electron charge measured in coulombs, and *m* is the mass of the electron. The orbital motion of the electron also gives rise to a magnetic dipole moment μ_{l} that is equal to μ_{0} when *l* = 1. *See* Magneton

The orbital magnetic moment of an electron can readily be deduced with the use of the classical statements of electromagnetic theory in quantum-mechanical theory; the simple classical analog of a current flowing in a loop of wire describes the magnetic effects of an electron moving in an orbit. The spin of an electron and the magnetic properties associated with it are, however, not possible to understand from a classical point of view.

In the Landé *g* factor, *g* is defined as the negative ratio of the magnetic moment, in units of μ_{0}, to the angular momentum, in units of ℏ. For the orbital motion of an electron, *g*_{l} = 1. For the spin of the electron the appropriate *g* value is *g*_{s} ≃ 2; that is, unit spin angular momentum produces twice the magnetic moment that unit orbital angular momentum produces. The total electronic magnetic moment of an atom depends on the state of coupling between the orbital and spin angular momenta of the electron.

#### Atomic beam measurements

With the development of spectroscopy by the atomic beam method, a new order of precision in the measurement of the frequencies of spectral lines became possible. By using the atomic-beam techniques, it became possible to measure *g*_{s}/*g*_{l} directly, with the result *g*_{s}/*g*_{l} = 2(1.001168 ± 0.000005). The magnetic moment of the electron therefore is not μ_{0} but 1.001168μ_{0}, or equivalently the *g* factor of the electron departs from 2 by the so-called *g* factor anomaly defined as *a* = (*g*_{2} - 2)/2 so that μ = (1 + *a*)_{0}. Thus the first molecular beam work gave *a* = 0.001168. *See* Molecular beams

#### Calculation of g-factor anomaly

It is not possible to give a qualitative description of the effects which give rise to the *g*-factor anomaly of the electron. The detailed theoretical calculation of the quantity is in the domain of quantum electrodynamics, and involves the interaction of the zero-point oscillation of the electromagnetic field with the electron. Comparison of theoretical determination of *a* with its experimental measurement constitutes the most accurate and direct existing test of the theory of quantum electrodynamics. *See* Atomic structure and spectra, Gyromagnetic ratio, Quantum electrodynamics, Quantum mechanics