electron orbital

An electron orbital (often referred to as just orbital) is a wave-like description of a potential position of an electron comprising part of an atom (atomic orbital) or molecule (molecular orbital). The term orbital derives from the idea of the electron orbiting the nucleus, but quantum mechanics doesn't model it as a planet-like orbit, but as a standing wave. Quantum mechanics limits the possible ways an electron can be bound to the nucleus, and the term orbital refers to which specific manner the electron can be bound. The orbital(s) occupied by the electron(s) of an atom comprise its state of excitation.

Each orbital is described by three quantum numbers, representing energy (principal quantum number), angular momentum (azimuthal quantum number), and the angular momentum vector (magnetic quantum number), termed n, l, and m respectively. (Spin is a fourth quantum number affecting electrons, designated m_s, a type of angular momentum associated with a single particle). A common designation for the first two quantum numbers of an orbital lists the numerical value of n followed by a letter code for l: s, p, d, and f for l=0, 1, 2, and 3 respectively. Thus the symbol 1s indicates n=1 and l=0. A superscript can be used to indicate the number of electrons in an atom with those numbers, e.g., 1s². The set of orbitals with a specific principal quantum number are known as a shell, i.e., electron shell.

Molecular orbitals are more complicated, with more ways an electron can be bound.

Specification of orbitals are used in spectrography to describe the specifics of the excitation or relaxation that produces a spectral line, e.g., a particular frequency of an emission line might be due to the relaxation of an electron from one specific orbital to another. Each orbital (for a specific nucleus) has an associated energy level (e.g., the binding energy of the electron in that orbital), and a photon emitted has the photon energy (thus the electromagnetic radiation frequency) equal to the energy-difference between the former and latter orbital. The energy level depends by far the most on n and a change in n is associated with a typical spectral line. For example Lyman alpha emission can be produced by an electron's fall from the state 2p to 1s. However there are slight differences in the electron's energy level due to other factors, such as differences in the other quantum numbers. For example, a change in spin, with other quantum numbers not changing, is the mechanism that produces the 21-cm line.

I have found the term electron orbital used with some differences: sometimes to refer an atom's location for two electrons (the orbital indicated by values of quantum numbers n and l, allowing two electrons within the orbital if they have different values of m) and elsewhere to refer to the atom's location for a single electron (the orbital indicated by values of all three quantum numbers, n, l, and m). This is merely different nomenclature, but something to be aware of.