Electron Configuration

Electron configuration refers to the distribution of electrons within the atomic or molecular orbitals of an element or compound. Each configuration specifies how electrons occupy quantum states defined by principal, azimuthal, magnetic and spin quantum numbers. These configurations play a central role in understanding atomic structure, the periodic table, chemical bonding and the behaviour of materials in both isolated and bulk systems. In quantum mechanics, each configuration corresponds to a particular energy level, and electrons may transition between configurations by absorbing or emitting photons.

Shells and Subshells

The concept of electron configuration originated with the Bohr model but was refined by quantum mechanics. Electrons occupy shells, defined by the principal quantum number n, where n is a positive integer. Each shell accommodates up to 2n22n^{2}2n2 electrons because of the doubling of available states arising from electron spin.
Within each shell, electrons occupy subshells defined by the azimuthal quantum number ℓ\ellℓ, where ℓ\ellℓ ranges from 0 to n−1n-1n−1. These subshells correspond to distinct orbital types:

• ℓ=0\ell = 0ℓ=0: s orbitals (2 electrons)
• ℓ=1\ell = 1ℓ=1: p orbitals (6 electrons)
• ℓ=2\ell = 2ℓ=2: d orbitals (10 electrons)
• ℓ=3\ell = 3ℓ=3: f orbitals (14 electrons)

These limits arise from the allowed combinations of magnetic and spin quantum numbers, subject to the Pauli exclusion principle, which holds that no two electrons in an atom may share all four quantum numbers simultaneously.
The wavefunctions of hydrogen-like atoms depend on spherical harmonics, giving rise to the characteristic shapes of the various orbital types. In multi-electron atoms, electron–electron repulsion and shielding effects modify energies but not the fundamental structure of shells and subshells.

Notation

Electron configurations are commonly expressed using subshell labels with superscripts indicating the number of electrons in each subshell. Examples include:

• Hydrogen: 1s11s^{1}1s1
• Lithium: 1s2 2s11s^{2}\, 2s^{1}1s22s1
• Phosphorus: 1s2 2s2 2p6 3s2 3p31s^{2}\, 2s^{2}\, 2p^{6}\, 3s^{2}\, 3p^{3}1s22s22p63s23p3

For elements with many electrons, the notation may be abbreviated by referencing the noble gas configuration of the previous period. For instance, phosphorus may be written as Ne 3s2 3p3\mathrm{Ne}\,3s^{2}\,3p^{3}Ne3s23p3.
Configurations for atoms in their ground states follow the Madelung energy-ordering rule, according to which subshells fill in order of increasing n+ℓn + \elln+ℓ. Thus, 4s is filled before 3d in neutral atoms, as seen in the sequence from argon to titanium. Spectroscopic ordering, which reflects the energies of subshells in ions or excited atoms, may differ; for instance, electrons are removed from 4s before 3d in transition metals.
It is conventional to omit superscript zeros for unoccupied subshells, although they may be explicitly included when discussing deviations from idealised filling patterns. Neutral palladium, for example, is often written as [Kr] 4d10[Kr]\,4d^{10}[Kr]4d10, omitting the empty 5s subshell.
The labels s, p, d and f originate from early spectroscopic classifications of fine-structure lines—sharp, principal, diffuse and fundamental. Subsequent orbitals follow alphabetical order (g, h, i, etc.), though these are seldom encountered outside theoretical contexts.

Ground and Excited States

The configuration with the lowest total electronic energy is the ground state. Excited states correspond to configurations in which one or more electrons occupy higher-energy orbitals. A familiar example is the sodium atom, whose ground-state configuration is 1s2 2s2 2p6 3s11s^{2}\,2s^{2}\,2p^{6}\,3s^{1}1s22s22p63s1. Promotion of the 3s electron to the 3p orbital forms the first excited state, underpinning the yellow emission (589 nm) of sodium vapour lamps as the atoms relax back to the ground state.
Excitation of core electrons is also possible but requires photons of much higher energy, typically in the X-ray region. Transitions between subshells within the same principal shell, or between valence subshells, dominate the spectroscopic characteristics of most atoms.

Molecular Electron Configurations

The electron configurations of molecules follow similar notation but use molecular orbital labels rather than atomic subshell labels. These molecular orbitals form through the combination of atomic orbitals during bond formation and are classified as bonding, antibonding or non-bonding. Molecular configuration determines geometric structure, reactivity and properties such as magnetism and absorption spectra.

Historical Background

The modern concept of electron configuration was shaped by early twentieth-century advances in atomic theory. Irving Langmuir’s 1919 work built on earlier ideas from Gilbert N. Lewis and Walther Kossel to propose arrangements of electrons consistent with observed chemical bonding patterns. Subsequent development of quantum mechanics, especially the introduction of the Schrödinger equation, enabled a rigorous description of atomic orbitals and subshell capacities. Slater determinants and configuration state functions later provided systematic ways to represent multi-electron wavefunctions.
Explicit quantum-mechanical treatments, including the role of electron correlation, are presented comprehensively in Robert D. Cowan’s foundational text on atomic structure. This work and others form the basis of current theoretical and computational approaches to the electron configurations of atoms, ions and molecules.