![]() The separations of the 2 n - 1 excited levels having the same n are largely determined by relativistic contributions, including the spin-orbit interaction, with the result that each of the n - 1 pairs of levels having the same j value is almost degenerate the separation of the two levels in each pair is mainly due to relatively small Lamb shifts. The hyperfine splitting of the 1H 1 s ground level results from the interaction of the proton and electron magnetic moments and gives rise to the famous 21 cm line. The Coulomb interaction between the nucleus and the single electron is dominant, so that the largest energy separations are associated with levels having different n. Written as a superscript, this number expresses the doublet character of the structure: each term for L ≥ 1 has two levels, with J = L ± 1/ 2, respectively. The multiplicity of the L term is equal to 2 S + 1 = 2 s + 1 = 2. The L values are written with the same letter code used for l values, but with roman capital letters. The latter notation is somewhat redundant for one-electron spectra, but is useful for consistency with more complex structures. A particular level is denoted either by nl j or by nl 2 L J with L = l and J = j. The quantum numbers n, l, and j are appropriate. ![]() The parity of a configuration is even or odd according to whether Σ il i is even or odd, the sum being taken over all electrons (in practice only those in open subshells need be considered). The 3 p 6 configuration thus represents a full subshell and 3 s 2 3 p 6 3 d 10 represents a full shell for n = 3. A subshell having this number of electrons is full, complete, or closed, and a subshell having a smaller number of electrons is unfilled, incomplete, or open. Thus the maximum number of equivalent electrons is 2(2 l + 1). ![]() The Pauli exclusion principle prohibits atomic states having two electrons with all four quantum numbers the same. for l = 3, 4, 5 ., the letter j being omitted. The numerical values of l are replaced by letters in writing a configuration, according to the code s, p, d for l = 0, 1, 2 and f, g, h . A configuration of several subshells is written as nl Nn′ l′ M . . The notation for a configuration of N equivalent electrons is nl N, the superscript usually being omitted for N = 1. Electrons having both the same n value and l value belong to a subshell, all electrons in a particular subshell being equivalent. Those electrons having the same principal quantum number n belong to the shell for that number. ![]() The central field approximation for a many-electron atom leads to wave functions expressed in terms of products of such one-electron states. The magnetic quantum numbers m l, m s, and m j represent the projections of the corresponding angular momenta along a particular direction thus, for example, m l = - l, - l + 1. The quantum number j represents the angular momentum obtained by coupling the orbital and spin angular momenta of an electron, i.e., j = l + s, so that j = l ± 1/ 2. The allowed values of n are the positive integers, and l = 0, 1. Atomic States, Shells, and ConfigurationsĪ one-electron atomic state is defined by the quantum numbers nlm lm s or nljm j, with n and l representing the principal quantum number and the orbital angular momentum quantum number, respectively.
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