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Four quantum numbers can describe an electron energy level in a hydrogen-like atom completely: Principal quantum number (n) Azimuthal quantum number (ℓ) Magnetic quantum number (m ℓ) Spin quantum number (m s) These quantum numbers are also used in the classical description of nuclear particle states (e.g. protons and neutrons).
The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the Pauli exclusion principle). These quantum numbers include the three that define orbitals, as well as the spin magnetic quantum number m s. Thus, two electrons may occupy a single orbital, so long as they have different values of m s.
As work continued on the electron shell structure of the Sommerfeld-Bohr Model, Sommerfeld had introduced three "quantum numbers n, k, and m, that described the size of the orbit, the shape of the orbit, and the direction in which the orbit was pointing." [23] Because we use k for the Boltzmann constant, the azimuthal quantum number was changed ...
This notation is used to specify electron configurations and to create the term symbol for the electron states in a multi-electron atom. When writing a term symbol, the above scheme for a single electron's orbital quantum number is applied to the total orbital angular momentum associated to an electron state.
In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. A CSF must not be confused with a configuration. In general, one configuration gives rise to several CSFs; all have the same total quantum numbers for spin and spatial parts but differ in their intermediate couplings.
[9] In 1924, E. C. Stoner incorporated Sommerfeld's third quantum number into the description of electron shells, and correctly predicted the shell structure of sulfur to be 2.8.6. [10] However neither Bohr's system nor Stoner's could correctly describe the changes in atomic spectra in a magnetic field (the Zeeman effect).
In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number (m l or m [a]) distinguishes the orbitals available within a given subshell of an atom.
The term "azimuthal quantum number" was introduced by Arnold Sommerfeld in 1915 [1]: II:132 as part of an ad hoc description of the energy structure of atomic spectra. . Only later with the quantum model of the atom was it understood that this number, ℓ, arises from quantization of orbital angular moment