Aufbau

Aufbau principle, from the German word Aufbau meaning "construction" or "building up," is a guideline in atomic theory for determining the ground-state electron configuration of atoms. It states that electrons fill available orbitals in order of increasing energy, subject to the Pauli exclusion principle and Hund's rule, so that the lowest-energy arrangement is produced.

In practice, the energy ordering of sublevels in atoms is often summarized by the Madelung rule, using the n + l value (principal quantum number plus azimuthal quantum number) to rank orbitals. When two orbitals have the same n + l, the one with the smaller n is filled first. This leads to the familiar sequence: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, and so on. In many elements the 4s subshell is filled before 3d, and the 3d and 4d orbitals may reorder as electrons are added.

In addition to providing a practical method for predicting ground-state configurations, the Aufbau principle is an approximation. Electron–electron interactions and relativistic effects can shift orbital energies, causing deviations from the simple pattern. Some elements show notable exceptions; for chromium and copper, the observed configurations are [Ar] 3d5 4s1 and [Ar] 3d10 4s1 respectively, reflecting extra stability of half-filled or filled subshells.

Historically, the principle emerged in the early 20th century as scientists developed quantum ideas to explain atomic spectra. Today, the Aufbau principle is widely used in chemistry and physics to assign electron configurations and to interpret periodic trends and chemical behavior.