Aufbau Principle or Sequence of energy levels

Aufbau is a German expression meaning ‘build up‘ or construction. This principle deals with the filling of electrons in different energy levels. This is also known as the ‘building up principle‘ or  ‘construction of an atom‘. According to this principle, protons are added to the nucleus and the electrons are added to orbitals one by one starting from the lowest available orbitals this addition is continued till all the electrons are equal in number to the nuclear charge (atomic number) and are safely accommodated.

In other words, orbitals are filled in order of their increasing energies. The configuration thus obtained corresponds to the stable state of the atom. Which is a given major energy level orbital it is found that the energy of these orbitals increases in increasing order and the order is s <  p <  d < f. For the higher energy levels, these differences are sufficiently pronounced that staggering of orbitals may result and the energy of the given orbital depends on the nuclear charge and different types of orbitals are affected to different degrees.

Thus, there is no single ordering of energies of orbitals correct for all elements. Nevertheless, the order is :

which is found to be extremely useful.
This complete order is not only correct for a single element, but it is also remarkably accurate for all elements. For the sake of simplicity, Moeller In 1952 suggested a “mnemonic diagram’ (figure 1.16) that gives the same order of energy levels.

 Madelung suggested that the above precise order which is followed in the filling up of the orbital is based on the principle quantum number ‘n‘ and the azimuthal quantum number ‘l‘. Using n and l values he was able to derive the same sequence of energy levels by applying the following rules :

1. The orbitals for which the value of (n + l) is lowest, are fined first by the electrons. Thus, the order of energies of the orbitals will obtain by increasing (n + l) values.
For example:

and so on.

2. When two or more orbitals have the same value, the one with the lower value of ‘n’ is filled first by the electrons. Thus, the order of increasing energies of such orbitals will be:

and so on.

Point to remember :

(a) In the Madelung rules, (n – l) describes the energy of the orbital with an increasing value of (n + l) energies of the orbitals also increase.

(b) The following order of the orbitals has been found to hold good for elements having atomic numbers below 90 i.e Z<90.

1s < 2s < 2p < 3p < 4s < 3d < 4p < 5s < 4d < 5d < 6s < 4f < 5d < 6p < 7s < 5f

and the sequence for the elements having atomic numbers above 90; Z > 90 is

1s < 2s < 2p < 3p < 4s < 3d < 4p < 5s < 4d < 5d < 6s < 4f < 5d < 6p < 7s < 5f < 6d........

Drawbacks of the Aufbau Principle :

1. The Aufbau principle is not able to predict the electronic configuration of atoms on ionization. In other words, It fails to describe which electrons are removed when a cation is formed from an atom. For example, according to the Aufbau principle, the configuration of  Fe(Z = 26) is 1s²,2s²2p⁶,3s²,3p⁶,4s²,3d⁶, it has been confirmed by the spectral and magnetic studies of  Fe²⁺ that  Fe³⁺ has configuration 1s²,2s²2p⁶,3s²,3p⁶,4s²,3d⁶, and not 1s²,2s²2p⁶,3s²,3p⁶,6s²,3d⁴, which shows that ionization cause the loss of electrons in preference to electrons even though the loss to be added in building up the configuration of Fe-atom.
2. The experimentally observed configurations of Cr(Z=24), Cu(Z=29), Mo(Z=42), Ag(Z=47), Gd(Z=79), Au(Z=79), and some other elements are anomalous, they can not be explained by Aufbau’s principle. The reason for these deviations is attributed to the extra stability associated with half-filled or completely-filled orbitals as suggested by Hund

3.   In the sixth period, 4f and 5 d sub-shells have approximately close energy. At lanthanum (Z = 57), the last electron does not go to the 4f sub-shell as predicted in the Aufbau principle but is added to the 5d sub-shell to give it a configuration : [Xe] 4f⁰5d¹6s². However, the next electron for cerium (Z = 58 ) is added to the 4f sub-shell and the electron of 5d goes to 4f to give it a configuration: [Xe]4/25d⁰6s².