n+l Rule for Atomic Electron Configurations

atomic number

show n + l

show configuration diagram

Orbitals in atomic ground-state electron configurations are filled in the order of increasing

n+l

. For equal

n+l

values, the orbital with the lower

is most often filled first. Here

is the principal quantum number

n=1,2,3,…

and

is the angular momentum quantum number

l=0,1,…,n-1

, designated by the code

for

l=0,1,2,3

, respectively. The "

n+l

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.

Details

Snapshot 1: electrons in degenerate orbitals enter with parallel spins until they are half-filled, in accordance with Hund's rule

Snapshot 2: for

Z=24

, 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 (

Z=57

), 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

External Links

Electron Configuration Browser

Permanent Citation

S. M. Blinder

"n+l Rule for Atomic Electron Configurations"
http://demonstrations.wolfram.com/NLRuleForAtomicElectronConfigurations/
Wolfram Demonstrations Project
Published: December 10, 2008