1.3:
Electron Configurations
The electron configuration of an atom represents the distribution of electrons among its atomic orbitals. The Pauli exclusion principle, Hund’s rule of maximum multiplicity, and the Aufbau principle can be extended to envisage the electron configuration of any element.
The Aufbau principle states that in the ground state, atomic orbitals fill in increasing order of energy. The relative energies of atomic orbitals are rationalized by Coulomb interactions, the shielding effect, and orbital penetration.
Consider the electron configuration for carbon—an element with atomic number six and thus neutral with six electrons. The 1s orbital, which has the lowest energy, is filled first.
According to the Pauli exclusion principle, no two electrons in an atom can have the same set of four quantum numbers. As electrons in the same orbital have the same principal, azimuthal, and magnetic quantum numbers, they must have different spin quantum numbers.
As the spin quantum number has only two possible values, an orbital can accommodate only two electrons, with opposite spins.
Though energy increases with shell number, the greater penetration of s orbitals lowers the energy of s orbitals relative to that of the p orbitals.
Therefore, the next two electrons occupy the 2s orbital and the fifth enters the 2p subshell. As orbitals within a subshell are presumed to be degenerate, the fifth electron can enter any of the three degenerate 2p orbitals.
The sixth electron follows Hund’s rule of maximum multiplicity and singly occupies a degenerate orbital rather than pairing. Hence, for carbon, the two 2p electrons occupy two different orbitals and have parallel spins.
The electron configuration diagram reveals that carbon has two electrons—called core electrons—in the inner shell and four electrons—called valence electrons—in the outermost shells.
The order of atomic orbitals relative to their energies can be remembered using such diagrams, where the path of the arrow reveals the sequence in which electrons are assigned to orbitals.
However, this progression becomes more complex as d and f orbitals are introduced and the sequence becomes less predictable for transition elements, lanthanides, and actinides.
1.3:
Electron Configurations
Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
The relative energies of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on). For various shells and subshells, the trend of penetrating power of an electron can be depicted as follows:
1s > 2s > 2p > 3s > 3p > 4s > 3d > 4p > 5s > 4d > 5p > 6s > 4f….
The effect of shielding and orbital penetration is large, and a 4s electron may have lower energy than a 3d electron.
Electrons in the outermost orbitals, called valence electrons, are responsible for most of the chemical behavior of elements. In the periodic table, elements with analogous valence electron configurations usually occur within the same group.
There are some exceptions to the predicted filling order, particularly when half-filled or completely filled orbitals can be formed. In the case of Cr and Cu, the half-filled and completely filled subshells apparently represent conditions of preferred stability. This stability is such that the electron shifts from the 4s into the 3d orbital to gain the extra stability of a half-filled 3d subshell (in Cr) or a filled 3d subshell (in Cu). Other exceptions also occur. For example, niobium (Nb, atomic number 41) is predicted to have the electron configuration [Kr]5s24d3. However, experimentally, its ground-state electron configuration is actually [Kr]5s14d4. We can rationalize this observation by saying that the electron–electron repulsions experienced by pairing the electrons in the 5s orbital are larger than the gap in energy between the 5s and 4d orbitals.
This text is adapted from Openstax, Chemistry 2e, Section 6.4: Electronic Structure of Atoms