What is the Madelung's rule?

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What is the Madelung's rule?

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Answer 1 · 2015-05-02T15:16:37

Madelung's rule states:

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

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

Identical values of $n + l$ $n+l$

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

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

Different $n + l$ $n+l$ values

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

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

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

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

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

$1 s$ $1s$ , $2 s 2 p$ $2s2p$ , $3 s 3 p$ $3s3p$ , $4 s 3 d 4 p$ $4s3d4p$ , $5 s 4 d 5 p$ $5s4d5p$ , $6 s 4 f 5 d 6 p$ $6s4f5d6p$ , $7 s 5 f 6 d 7 p$ $7s5f6d7p$ , $8 s 5 g 6 f 7 d 8 p$ $8s5g6f7d8p$ , $9 s \dots$ $9s…$

The order is summarized in the triangular diagram below.

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What is the Madelung's rule?

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