The central field approximation for a many-electron atom leads to wave functions expressed in terms of products of such one-electron states [2,3]. Those electrons having the same principal quantum number n belong to the shell for that number. Electrons having both the same n value and l value belong to a subshell, all electrons in a particular subshell being equivalent. The notation for a configuration of N equivalent electrons is nl N, the superscript usually being omitted for N = 1. A configuration of several subshells is written as nl Nn′l′ M ... . 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 ... for l = 3, 4, 5 ..., the letter j being omitted.
The Pauli exclusion principle prohibits atomic states having two electrons with all four quantum numbers the same. Thus the maximum number of equivalent electrons is 2(2l + 1). 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. The 3p6 configuration thus represents a full subshell and 3s2 3p6 3d10 represents a full shell for n = 3.
The parity of a configuration is even or odd according to
whether Σili is even or odd, the sum being
taken over all electrons (in practice only those in open subshells need be
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. The hyperfine splitting of the
1H 1s ground level
[1420.405 751 766 7(10) MHz] results from the interaction
of the proton and electron magnetic moments and gives rise to the famous
21 cm line. The separations of the 2n - 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.