### 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

(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 _{9}Cu to be 1s^{2}2s^{2}2p^{6}3s^{2} 3p^{6}4s^{2}3d^{9 }or [Ar]4s^{2}3d^{9} while the experimental configuration of a copper atom is [Ar]4s^{1}3d^{10}.

Filling the 3d orbital completely gives the copper atom a more stable configuration or lower energy state.