Chemistry - Aufbau principle

Aufbau principle : 

‘Aufbau’ is a German word meaning ‘building up’. The building up of orbital means filling up of orbitals with electrons in the ground state of an atom. The aufbau principle is based on,

(i) Increasing order of energies of orbitals,
(ii) Pauli’s exclusion principle,
(iii) Hund’s rule of maximum multiplicity

Inceasing order of orbital energy

i. The increasing order of energies of orbitals :

The increasing order of energies of obitals is decided by the (n + l) value. Electrons in the ground state atom are filled in the orbitals in an increasing order of energy. Figure shows a useful method to remember this increasing order of orbital energy.

ii. Pauli exclusion principle : 

The capacity of an orbital to accommodate electrons is decided by Pauli exclusion principle. Wolfgang Pauli (1926) recognized that “No two electrons in an atom can have the same set of four quantum numbers.” Another way to state this Pauli exclusion principle is: “Only two electrons can occpy the same orbital and they must have opposite spins.” Pauli exclusion principle implies that for an electron belonging to the same orbital, the spin quantum number ‘ms’ must be different since the other three quantum numbers n, l and ml

 are the same. There are only two values that ‘ms’ can which are +1/2 and -1/2. An orbital thus can accommodate only two electrons with opposite spins, so that the fourth quantum number is different for two occupying electrons. These two electrons with opposite spins occupying the same orbital are called an electron pair. This principle is illustrated with helium atom He (Z = 2). Its electronic configuration is 1s2 as. 

And two electrons are in 1s orbital. The two non - identical combinations of the four quantum numbers of both electrons in helium are given in Table.

Table

Since an orbital can accommodate up to two electrons only, the capacity of a shell with the principal quantum number n, to accommolate electrons is given by 2n2.

iii. Hund’s rule of maximum multiplicity : 

Filling of electrons in the orbitals belonging to the same subshell (orbitals of equal energy or degenerate orbitals) follows the Hund’s rule of maximum multiplicity. As per this rule “Pairing of electrons in the orbitals belonging to the same subshell does not occur unless each orbital belonging to that subshell has got one electron each.” Consider, for example, filling of p subshell. The p subshell has three degenerate orbitals. Here pairing of electrons starts when the fourth electron enters the p subshell. The electronic configuration of four electrons occupying p-orbital then will beand not as. It is observed that half-filled and fully filled set of degenerate orbitals has extra stability.