Aufbau Principle


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The Aufbau principle states that in the ground state of an atom, an electron enters the orbital of lowest energy first, and then the subsequent electrons are fed in the order of increasing energies into the orbitals. The relative energies of various orbitals are given in fig.1.6. From the figure, the following sequence is observed for orbitals in the increasing energy:1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s.

According to Aufbau principle, the orbitals should be filled in the above sequence. It is very important to remember that the sequence of energy levels pertains up to 3p and then 4s orbital comes first instead of 3d. In fact the energy of an orbital is determined by the quantum numbers n and l with the help of important rule known as (n + l) rule or Bohr Bury's rule.

According to this

(i) in neutral atoms, the orbital with lower value of (n + l) has lower energy than the orbital with higher (n +l) value.

(ii) if two orbitals have the same value of (n + l) then the orbital with lower value of n has lower energy.

For e.g., 3s-orbital (n + l = 3 + 0 = 3) possesses lower energy than 3p (n + l = 3 + 1 = 4) orbital.

Similarly 2p-orbital (n + l = 2 + 1 = 3) and 3s-orbital (n + l = 3 + 0 = 3) have the same (n + l) value, but 2p-orbital has lower value of n and, therefore, is lower in energy than 3s-orbital [(Rule (ii)].

This rule also helps to account for the fact that certain orbitals with higher value of n but lower value of l have less energy than orbital with lower value of n and higher value of l. For e.g., if 4s- and 3d-orbitals are considered, for 3d-orbital (n + l) value = 3 + 2 = 5 while for 4s-orbital. (n + l) value = 4 + 0 = 4. Thus. 4s-orbital has lesser energy than 3d-orbital.

The sequence of energy levels can be easily remembered by the systematic diagram as shown in the figure given below.

systematic diagram of sequence of energy levels

fig 1.7 - Sequence of filling atomic orbitals


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