Wiswesser's rule

The Wiswesser rule gives a simple method to determine the energetic sequence of the atomic subshells ( n , l ) . n is the principal quantum number and l is the azimuthal quantum number. The energetic sequence of the subshells characterized by the quantum numbers ( n , l ) is the sequence that leads to a monotonically increasing row of function values for the Wiswesser function.

For example: if n = 2 and l = 1 , this corresponds to a 2p-orbital.

If the results of this function for each shell and subshell are ordered, the resulting sequence is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p...

To illustrate this, the corresponding values of each of these shells can be found in the table below:

We can now clearly see that the Aufbau principle and Wiswesser's Rule come to the same order of filling electron shells.