Everything about Spin Quantum Number totally explained
In
atomic physics, the
spin quantum number is a
quantum number that parameterizes the intrinsic
angular momentum (or spin angular momentum, or simply
spin) of a given
particle. The
spin quantum number is the fourth of a set of
quantum numbers (the
principal quantum number, the
azimuthal quantum number, the
magnetic quantum number, and the spin quantum number) which describe the unique
quantum state of an electron and is designated by the letter
s.
Derivation
As a quantized angular momentum, (see
angular momentum quantum number) it holds that
»
where
» g is the Lande g-factor
is the
Bohr magneton
When atoms have even numbers of electrons the spin of each electron in each orbital has opposing orientation in different directions. However, many atoms have an odd number of electrons or an arrangement of electrons in which the number of "spin-up" and "spin-down" orientations are not the same. These atoms or electrons are said to have unpaired spins which are detected in
electron spin resonance.
Detection of spin
When the spectral lines of the hydrogen spectrum are examined at very high resolution, they're found to be closely-spaced doublets. This splitting is called fine structure and was one of the first experimental evidences for electron spin. The direct observation of the electron's intrinsic angular momentum was achieved in the
Stern-Gerlach experiment.
Dirac equation solves spin
When the idea of electron spin was first introduced in 1925, even Wolfgang Pauli had trouble accepting
Ralph Kronig's model. The problem wasn't that a rotating charged particle would have given rise to a magnetic field, but that the electron was so small that the equatorial speed of the electron would have to be greater than the speed of light for the magnetic moment to be of the observed strength.
In 1930,
Paul Dirac developed a new version of the Schrödinger Wave Equation which was relativistically invariant, and predicted the magnetic moment correctly, and at the same time treated the electron as a point particle. In the
Dirac equation all four quantum numbers including the additional quantum number
s arose naturally during its solution.
Further Information
Get more info on 'Spin Quantum Number'.
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