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For example, one can exert a kind of "torque" on an electron by putting it in a magnetic field (the field acts upon the electron's intrinsic magnetic dipole moment—see the following section). The result is that the spin vector undergoes precession, just like a classical gyroscope. This phenomenon is known as electron spin resonance (ESR).
The atom would then be pulled toward or away from the stronger magnetic field a specific amount, depending on the value of the valence electron's spin. When the spin of the electron is + + 1 / 2 the atom moves away from the stronger field, and when the spin is − + 1 / 2 the atom moves toward it. Thus the beam of silver atoms is ...
The spinning electron model here is analogous to a gyroscope. For any rotating body the rate of change of the angular momentum equals the applied torque : =. Note as an example the precession of a gyroscope. The earth's gravitational attraction applies a force or torque to the gyroscope in the vertical direction, and the angular momentum vector ...
Here is a negative constant multiplied by the spin, so the spin magnetic moment is antiparallel to the spin. The spin–orbit potential consists of two parts. The Larmor part is connected to the interaction of the spin magnetic moment of the electron with the magnetic field of the nucleus in the co-moving frame of the electron.
If does not equal , the implication is that the ratio of the unpaired electron's spin magnetic moment to its angular momentum differs from the free-electron value. Since an electron's spin magnetic moment is constant (approximately the Bohr magneton), then the electron must have gained or lost angular momentum through spin–orbit coupling ...
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry.
Note that μ is a negative constant multiplied by the spin, so the magnetic moment is antiparallel to the spin angular momentum. The spin g-factor g s = 2 comes from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties. Reduction of the Dirac equation for an electron in a magnetic field ...
With one unpaired electron μ eff values range from 1.8 to 2.5 μ B and with two unpaired electrons the range is 3.18 to 3.3 μ B. Note that low-spin complexes of Fe 2+ and Co 3+ are diamagnetic. Another group of complexes that are diamagnetic are square-planar complexes of d 8 ions such as Ni 2+ and Rh + and Au 3+.