atomorbital

Atomorbital, more commonly called the atomic orbital, is a region in space around an atom where there is a high probability of locating an electron. In quantum mechanics, atomic orbitals are described by wavefunctions ψnlm(r, θ, φ) that solve the Schrödinger equation for electrons in an atomic potential. Each orbital is labeled by quantum numbers: principal n, azimuthal l, and magnetic m, with a spin quantum number s for the electron’s spin. The orbital can be written as ψnlm(r, θ, φ) = Rnl(r)Ylm(θ, φ), where Rnl is the radial function and Ylm are spherical harmonics. The square modulus |ψ|^2 gives the electron density.

Orbitals come in sets with characteristic shapes: s orbitals (l = 0) are spherical; p orbitals (l = 1) are dumbbell-shaped along three axes; d (l = 2) and f (l = 3) orbitals have more complex geometries. Each orbital can hold up to two electrons with opposite spins, in accordance with the Pauli exclusion principle.

In hydrogen-like atoms, orbital energy depends primarily on the principal quantum number n. In multi-electron atoms, energies depend on both n and l due to electron–electron repulsion and shielding, leading to ordering schemes described by the Aufbau principle and the n + l rule, with occasional deviations.

Atomic orbitals underpin electron configurations, valence chemistry, and bonding. They form the basis for molecular orbital theory and hybridization, explaining molecular shapes and reactivity. Although the term atomorbital is sometimes used as an alternative spelling, the standard term remains atomic orbital. See also atomic and molecular orbital concepts.