Atomic orbital

In quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function describes an electron's charge distribution around the atom's nucleus, and can be used to calculate the probability of finding an electron in a specific region around the nucleus.

Each orbital in an atom is characterized by a set of values of three quantum numbers n, ℓ, and mℓ, which respectively correspond to an electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis (magnetic quantum number). The orbitals with a well-defined magnetic quantum number are generally complex-valued. Real-valued orbitals can be formed as linear combinations of mℓ and −mℓ orbitals, and are often labeled using associated harmonic polynomials (e.g., xy, x2 − y2) which describe their angular structure.

An orbital can be occupied by a maximum of two electrons, each with its own projection of spin

m

s

{\displaystyle m_{s}}

. The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number ℓ = 0, 1, 2, and 3 respectively. These names, together with their n values, are used to describe electron configurations of atoms. They are derived from description by early spectroscopists of certain series of alkali metal spectroscopic lines as sharp, principal, diffuse, and fundamental. Orbitals for ℓ > 3 continue alphabetically (g, h, i, k, ...), omitting j because some languages do not distinguish between letters "i" and "j".