Question

What is the Madelung's rule?

Answer 1

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.