An atomic orbital is a mathematical function that describes the wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term may also refer to the physical region defined by the function where the electron is likely to be.

Specifically, atomic orbitals are the possible quantum states of an individual electron in the electron cloud around a single atom, as described by the function. The term "orbital" was coined by Robert Mulliken in 1932. However, the idea that electrons might revolve around a compact nucleus with definite angular momentum was convincingly argued at least 19 years earlier by Niels Bohr, and the Japanese physicist Hantaro Nagaoka published an orbit-based hypothesis for electronic behavior as early as 1904.

Explaining the behavior of these electron "orbits" was one of the driving forces behind the development of quantum mechanics. Atomic orbitals are typically described as hydrogen-like wave functions over space, indexed by the n, l, and m quantum numbers or by the names used in electron configurations, as shown on the right. Despite the obvious analogy to planets revolving around the Sun, electrons cannot be described as solid particles and so atomic orbitals rarely, if ever, resemble a planet's elliptical path.

A more accurate analogy might be that of a large and often oddly-shaped atmosphere (the electron), distributed around a relatively tiny planet (the atomic nucleus). Because of the difference from classical mechanical orbits, the term "orbit" for electrons in atoms, has been replaced with the term orbital. The orbital names (s, p, d, f) are derived from the characteristics of their spectroscopic lines: sharp, principal, diffuse, and fundamental, the rest being named in alphabetical order.

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