The aufbau principle

Ground state electronic configurations

  In the previous two sections, we have considered experimental electronic configurations and have seen that the organization of the elements in the periodic table depends on the number, and arrangement, of electrons that each element possesses. Establishing the ground state electronic configuration of an atom is the key to understanding its chemistry, and we now discuss the aufbau principle (aufbau means ‘building up’ in German) which is used in conjunction with Hund’s rules and the Pauli exclusion principle to determine electronic ground state configurations:

• Orbitals are filled in order of energy, the lowest energy orbitals being filled first.
• Hund’s first rule (often referred to simply as Hund’s rule): in a set of degenerate orbitals, electrons may not be spin-paired in an orbital until each orbital in the set contains one electron; electrons singly occupying orbitals in a degenerate set have parallel spins, i.e. they have the same values of ms.
•  Pauli exclusion principle: no two electrons in the same atom may have the same set of n, Ɩ, m_Ɩ and m_s quantum numbers; it follows that each orbital can accommodate a maximum of two electrons with different m_s values (different spins = spin-paired).

• Worked example 1.5 Using the aufbau principle

  Determine (with reasoning) the ground state electronic configurations of (a) Be (Z = 4) and (b) P (Z = 15).

  The value of Z gives the number of electrons to be accommodated in atomic orbitals in the ground state of

  the atom.

  Assume an order of atomic orbitals (lowest energy first) as follows: 1s < 2s < 2p < 3s < 3p

  (a) Be Z = 4    Two electrons (spin-paired) are accommodated in the lowest energy 1s atomic orbital.

    The next two electrons (spin-paired) are accommodated in the 2s atomic orbital. The ground state electronic configuration of Be is therefore 1s² 2s².

  (b) P Z = 15  Two electrons (spin-paired) are accommodated in the lowest energy 1s atomic orbital.

  The next two electrons (spin-paired) are accommodated in the 2s atomic orbital.

  The next six electrons are accommodated in the three degenerate 2p atomic orbitals, two spin-paired electrons per orbital. The next two electrons (spin-paired) are accommodated in the 3s atomic orbital.

  Three electrons remain and applying Hund’s rule, these singly occupy each of the three degenerate 3p atomic orbitals. The ground state electronic configuration of P is therefore

  1s² 2s² 2p⁶ 3s² 3p³.