n+l Rule for Atomic Electron Configurations
Orbitals in atomic ground-state electron configurations are filled in the order of increasing . For equal values, the orbital with the lower is most often filled first. Here is the principal quantum number and is the angular momentum quantum number , designated by the code , , , for , respectively. The " rule," also known as the Madelung rule or the diagonal rule, holds with only a small number of irregularities. The designation "diagonal rule" refers to the pattern of atomic orbitals shown in the graphic. The optional configuration diagram also shows the spins of the electrons in occupied orbitals. In accord with the Pauli exclusion principle, each orbital has a maximum capacity of two electrons, with opposite spins. The actual electron configurations are deduced from spectroscopic and chemical characteristics. This Demonstration covers the naturally occurring elements with atomic numbers from 1 to 92.
Snapshot 1: electrons in degenerate orbitals enter with parallel spins until they are half-filled, in accordance with Hund's rule
Snapshot 2: for , an electron from the orbital jumps to to produce a half-filled -shell with an enhanced number of parallel spins
Snapshot 3: after a single -electron in lanthanum (), the orbitals begin to fill in the lanthanides (or rare earths)
Snapshot 4, 5, 6: the electron configurations of Ni, Pd and Pt, although in the same column of the periodic table, give a well-known counterexample to simple generalizations
Reference: S. M. Blinder, Introduction to Quantum Mechanics, Amsterdam: Academic Press, 2004 pp. 126–130