7.15: Electron Configuration of Multielectron Atoms

The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the 3s orbital, giving a 1s²2s²2p⁶3s¹ configuration. The electrons occupying the outermost shell orbital(s) (highest value of n) are called valence electrons, and those occupying the inner shell orbitals are called core electrons. Since the core electron shells correspond to noble gas electron configurations, we can abbreviate electron configurations by writing the noble gas that matches the core electron configuration, along with the valence electrons in a condensed format. For sodium, the symbol [Ne] represents core electrons, (1s²2s²2p⁶), and the abbreviated or condensed configuration is [Ne]3s¹.

Similarly, the abbreviated configuration of lithium can be represented as [He]2s¹, where [He] represents the configuration of the helium atom, which is identical to that of the filled inner shell of lithium. Writing the configurations in this way emphasizes the similarity of the configurations of lithium and sodium. Both atoms, which are in the alkali metal family, have only one electron in a valence s subshell outside a filled set of inner shells.

Li: [He]2s¹

Na: [Ne]3s¹

The alkaline earth metal magnesium (atomic number 12), with its 12 electrons in a [Ne]3s² configuration, is analogous to its family member beryllium, [He]2s². Both atoms have a filled s subshell outside of their filled inner shells. Aluminum (atomic number 13), with 13 electrons and the electron configuration [Ne]3s²3p¹, is analogous to its family member boron, [He]2s²2p¹.

The electron configurations of silicon (14 electrons), phosphorus (15 electrons), sulfur (16 electrons), chlorine (17 electrons), and argon (18 electrons) are analogous in the electron configurations of their outer shells to their corresponding family members carbon, nitrogen, oxygen, fluorine, and neon, respectively, except that the principal quantum number of the outer shell of the heavier elements has increased by one to n = 3.

When we come to the next element in the periodic table, the alkali metal potassium (atomic number 19), we might expect that we would begin to add electrons to the 3d subshell. However, all available chemical and physical evidence indicates that potassium is like lithium and sodium, and that the next election is not added to the 3d level but is, instead, added to the 4s level. As discussed previously, the 3d orbital with no radial nodes is higher in energy because it is less penetrating and more shielded from the nucleus than the 4s, which has three radial nodes. Thus, potassium has an electron configuration of [Ar]4s¹. Hence, potassium corresponds to Li and Na in its valence shell configuration. The next electron is added to complete the 4s subshell and calcium has an electron configuration of [Ar]4s². This gives calcium an outer-shell electron configuration corresponding to that of beryllium and magnesium.

In the case of Cr and Cu, we find that half-filled and completely filled subshells apparently represent conditions of preferred stability. This stability is such that 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. Experimentally, we observe that its ground-state electron configuration is actually [Kr]5s¹4d ⁴. 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. There is no simple method to predict the exceptions for atoms where the magnitude of the repulsions between electrons is greater than the small differences in energy between subshells.

This text is adapted from Openstax, Chemistry 2e, Section 6.4: Electronic Structure of Atoms.

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.

Consider writing the electron configuration for sodium. The core electron distribution in sodium is exactly that of the preceding element, neon. The single valence electron occupies the 3s orbital.

Neon belongs to the eighteenth column of the periodic table — the noble gases. The electron configurations of these elements facilitate the condensed depiction of the electron configuration for other elements. For any element, the core electron configuration is the same as that of the noble gas that precedes it in the periodic table.

The electron configuration of sodium, for example, can be written as neon core, 3s¹.

The core electron configuration of potassium is 1s² 2s² 2p⁶ 3s² 3p⁶, leaving one valence electron. Now, does the nineteenth electron enter the 3d subshell? 

Recall that the 4s subshell has substantial penetrating ability, which often leads to it having a lower energy than the 3d subshell does. The aufbau principle, therefore, would hold that the 4s subshell fills prior to the 3d subshell. The core of the preceding noble gas, argon, is used to write the condensed configuration.

Although these principles provide a starting point, the actual electron configurations must be confirmed experimentally. In several elements among the transition elements, lanthanides, and actinides, the orbital energies are in a different relative order, and the aufbau principle may not be completely followed.

In the transition elements, the 3d and 4s subshells have similar energies. The 4s subshell is often filled completely. For example, in scandium, the electron configuration is argon core, 4s² 3d¹. In zinc, the 4s and 3d subshells are filled to their maximum capacities.

However, the ground states of some metals, such as chromium and copper, have singly occupied 4s orbitals. Chromium is particularly notable because two subshells are partially filled, which deviates from the aufbau principle.
Across the lanthanide series, extending through cerium to lutetium, the 6s and 4f subshells have similar energies. The electron configuration for neodymium is xenon core, 6s² 4f⁴. 

Meanwhile, cerium has an unusual electron configuration of xenon core, 6s² 4f¹ 5d¹ because its 6s, 4f, and 5d subshells are unusually close in energy.