What is the Madelung's rule?

1 Answer
Ernest Z.
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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