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A quantum number beginning in n = 3,ℓ = 0, describes an electron in the s orbital of the third electron shell of an atom. In chemistry, this quantum number is very important, since it specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles. The azimuthal quantum number can also denote the number of ...
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
For example, the "4s subshell" is a subshell of the fourth (N) shell, with the type (s) described in the first row. The second column is the azimuthal quantum number (ℓ) of the subshell. The precise definition involves quantum mechanics, but it is a number that characterizes the subshell.
The numbers of electrons that can occupy each shell and each subshell arise from the equations of quantum mechanics, [a] in particular the Pauli exclusion principle, which states that no two electrons in the same atom can have the same values of the four quantum numbers.
The subshell types are characterized by the quantum numbers. Four numbers describe an orbital in an atom completely: the principal quantum number n, the azimuthal quantum number ℓ (the orbital type), the orbital magnetic quantum number m ℓ, and the spin magnetic quantum number m s. [39]
However there are numerous exceptions; for example the lightest exception is chromium, which would be predicted to have the configuration 1s 2 2s 2 2p 6 3s 2 3p 6 3d 4 4s 2, written as [Ar] 3d 4 4s 2, but whose actual configuration given in the table below is [Ar] 3d 5 4s 1.
The maximum number of electrons in a subshell is equal to 2(2 l + 1), where the azimuthal quantum number l is equal to 0, 1, 2, and 3 for s, p, d, and f subshells, so that the maximum numbers of electrons are 2, 6, 10, and 14 respectively.
Grayed out electron numbers indicate subshells filled to their maximum. Bracketed noble gas symbols on the left represent inner configurations that are the same in each period. Written out, these are: He, 2, helium : 1s 2 Ne, 10, neon : 1s 2 2s 2 2p 6 Ar, 18, argon : 1s 2 2s 2 2p 6 3s 2 3p 6 Kr, 36, krypton : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 ...