What is the Madelung's rule?

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Answer 1 · 2015-05-02T15:16:37

Madelung's rule states:

where $n$ is the principal quantum number and $l$ is the azimuthal quantum number.

Identical values of $n+l$

For a $2p$ orbital, $n+l = 3$ ; for a $3s$ orbital, $n+l = 3$ . So $2p < 3s$ .

If there are identical $n+l$ values, the orbital with a lower $n$ value is filled first.

Different $n+l$ values

For a $3d$ orbital, $n+ l = 5$ ; for a $4s$ orbital, $n+l = 4$ , so $4s < 3d$ .

If there are different $n+l$ values, the orbital with a lower $n+l$ value is filled first.

This order is based on the total number of nodes in the atomic orbital, $n+l$ .

The higher the value of $l$ , the more nodes, and the higher the energy of the orbital.

The complete order for filling orbitals according to the Madelung rule is:

$1s$ , $2s2p$ , $3s3p$ , $4s3d4p$ , $5s4d5p$ , $6s4f5d6p$ , $7s5f6d7p$ , $8s5g6f7d8p$ , $9s…$

The order is summarized in the triangular diagram below.

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