Orbital Definition and Example

Orbital Definition

In chemistry and quantum mechanics, an orbital is a mathematical function that describes the wave-like behavior of an electron, electron pair, or (less commonly) nucleons. An orbital may also be called an atomic orbital or electron orbital. Although most people think of an "orbit" regarding a circle, the probability density regions that may contain an electron may be spherical, dumbbell-shaped, or more complicated three-dimensional forms.

The purpose of the mathematical function is to map the probability of the location of an electron in a region around (or theoretically inside) an atomic nucleus.

An orbital may refer to an ​electron cloud having an energy state described by given values of the n, ℓ, and m_ℓ quantum numbers. Every electron is described by a unique set of quantum numbers. An orbital can contain two electrons with paired spins and is often associated with a specific region of an atom. The s orbital, p orbital, d orbital, and f orbital refer to orbitals that have an angular momentum quantum number ℓ = 0, 1, 2, and 3, respectively. The letters s, p, d, and f come from the descriptions of alkali metal spectroscopy lines as appearing sharp, principal, diffuse, or fundamental. After s, p, d, and f, orbital names beyond ℓ = 3 are alphabetical (g, h, i, k, ...). The letter j is omitted because it isn't different from i in all languages.

Orbital Examples

The 1s² orbital contains two electrons. It is the lowest energy level (n = 1), with an angular momentum quantum number ℓ = 0.

The electrons in the 2p_x orbital of an atom are generally found within a dumbbell-shaped cloud about the x-axis.

Properties of Electrons in Orbitals

Electrons display wave-particle duality, which means they exhibit some properties of particles and some characteristics of waves.

Particle Properties

• Electrons have particle-like properties. For example, a single electron has a -1 electrical charge.
• There are an integer number of electrons around an atomic nucleus.
• Electrons move between orbitals like particles. For example, if a photon of light is absorbed by an atom, only a single electron changes energy levels.

Wave Properties

At the same time, electrons behave like waves.

• Although it's common to think of electrons as individual solid particles, in many ways they are more like a photon of light.
• It's not possible to pinpoint the location of an electron, only describe the probability of finding one within a region described by a wave function.
• Electrons don't orbit the nucleus like Earth orbits the Sun. The orbit is a standing wave, with the energy levels like harmonics on vibrating string. An electron's lowest energy level is like the fundamental frequency of a vibrating string, while higher energy levels are like harmonics. The region that might contain an electron is more like a cloud or atmosphere, except a spherical probability only applies when an atom only has a single electron!

Orbitals and the Atomic Nucleus

Although discussions about orbitals almost always refer to electrons, there are also energy levels and orbitals in the nucleus. The different orbitals give rise to nuclear isomers and metastable states.