What is the Madelung's rule?

1 Answer
May 2, 2015

Madelung's rule states:

  1. The energy of an atomic orbital increases with increasing n + l
  2. For identical values of n + l, energy increases with increasing n

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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