Madelung's Rule Definition

Madelung's Rule Definition

Madelung's rule describes electron configuration and the filling of atomic orbitals. The rule states:

(1) Energy increases with increasing n + l

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Introduction to the Aufbau Principle in Chemistry

By Todd Helmenstine

(2) For identical values of n + l, energy increases with increasing n

The following order for filling orbitals results:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, (8s, 5g, 6f, 7d, 8p, and 9s)

The orbitals listed in parentheses are not occupied in the ground state of the heaviest atom known, Z = 118. The reason orbitals fill this way is because the inner electrons shield the nuclear charge. Orbital penetration is as follows:
s > p > d >f

Madelung's rule or Klechkowski's rule originally was described by Charles Janet in 1929 and rediscovered by Erwin Madelung in 1936. V.M. Klechkowski described the theoretical explanation of Madelung's rule. The modern Aufbau principle is based on Madelung's rule.

Also Known As: Klechkowski's rule, Klechowsy rule, diagonal rule, Janet rule

Exceptions to Madelung's Rule

Keep in mind, Madelung's rule may only be applied to neutral atoms in the ground state. Even then, there are exceptions from the ordering predicted by the rule and experimental data. For examples, the observed electron configurations of copper, chromium, and palladium are different from predictions. The rule predicts the configuration of ₉Cu to be 1s²2s²2p⁶3s² 3p⁶4s²3d⁹ or [Ar]4s²3d⁹ while the experimental configuration of a copper atom is [Ar]4s¹3d¹⁰. Filling the 3d orbital completely gives the copper atom a more stable configuration or lower energy state.