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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
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 angular nodes present in an orbital. For example, for p orbitals, ℓ = 1 and thus the amount of angular nodes in a p orbital is 1.
Orbitals of the Radium. (End plates to [1]) 5 electrons with the same principal and auxiliary quantum numbers, orbiting in sync. ([2] page 364) The Sommerfeld extensions of the 1913 solar system Bohr model of the hydrogen atom showing the addition of elliptical orbits to explain spectral fine structure.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... m ℓ = azimuthal magnetic quantum number; j = total angular momentum quantum number;
This is often useful, and the values are characterized by the azimuthal quantum number (l) and the magnetic quantum number (m). In this case the quantum state of the system is a simultaneous eigenstate of the operators L 2 and L z, but not of L x or L y. The eigenvalues are related to l and m, as shown in the table below.
The four quantum numbers n, ℓ, m, and s specify the complete and unique quantum state of a single electron in an atom, called its wave function or orbital. Two electrons belonging to the same atom cannot have the same values for all four quantum numbers, due to the Pauli exclusion principle .
Download as PDF; Printable version ... the principal quantum number n is n 2-fold ... where is the azimuthal (angular momentum) quantum number. For instance, the ...
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.