Atomic Orbital
An atomic orbital is a mathematical function describing the wave-like behaviour and probable location of an electron in an atom, representing a region of space where there is a high probability (typically 90–95%) of finding the electron. Orbitals are characterised by three quantum numbers (n, l, mₗ) and have distinct shapes: s-orbitals are spherical, p-orbitals are dumbbell-shaped, and d- and f-orbitals have more complex geometries. Atomic orbitals form the basis for understanding electron configurations, chemical bonding, and molecular orbital theory.
Properties of Atomic Orbitals by Subshell Type
| Orbital Type | l value | Shape | Number per Subshell | Max Electrons |
|---|---|---|---|---|
| s | 0 | Spherical | 1 | 2 |
| p | 1 | Dumbbell (3 lobes) | 3 | 6 |
| d | 2 | Cloverleaf / complex | 5 | 10 |
| f | 3 | Complex multi-lobe | 7 | 14 |
| g | 4 | Highly complex | 9 | 18 |
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Related Terms
Quantum Number
Quantum numbers are discrete integer or half-integer values that characterise the quantum state of an electron (or other quantum particle) in an atom, arising naturally as solutions to the Schrödinger equation. The four quantum numbers for electrons — principal (n), azimuthal (l), magnetic (mₗ), and spin (mₛ) — together uniquely specify the quantum state of each electron in accordance with the Pauli Exclusion Principle. They determine the energy, shape, spatial orientation, and spin of atomic orbitals, providing the foundation for the periodic table and chemical bonding.
Wave Function
The wave function (denoted Ψ) is a mathematical function in quantum mechanics that completely describes the quantum state of a particle or system. Its squared modulus |Ψ|² gives the probability density for finding the particle at a given position and time, as interpreted by Max Born in 1926. The wave function must be continuous, single-valued, and square-integrable (normalised so that the total probability integrates to one), and it evolves deterministically according to the Schrödinger equation.
Electron Spin
Electron spin is an intrinsic quantum mechanical property of electrons (and other fermions) that represents a form of angular momentum with no classical analogue — the electron does not physically rotate, but behaves as if it does, with a fixed magnitude of angular momentum. Electrons have a spin quantum number s = 1/2, giving two possible spin states: spin-up (mₛ = +1/2) and spin-down (mₛ = −1/2). Electron spin is responsible for the Pauli Exclusion Principle, magnetic properties of atoms (paramagnetism and diamagnetism), and is the basis for technologies such as MRI and spintronics.
The term "orbital" was coined by American chemist Robert Mulliken in 1932, derived from "orbit" (Latin "orbita", track or course), to distinguish the quantum mechanical concept from Bohr's classical planetary orbits. The concept replaced Bohr's circular orbits after the development of wave mechanics in 1926.