elektronorbital

An elektronorbital, or electron orbital, is a mathematical function that describes the region around an atom’s nucleus where there is a high probability of finding an electron. In quantum mechanics, orbitals are solutions to the Schrödinger equation for electrons in the nuclear potential (and in real atoms, the additional effects of electron–electron interaction). They are not fixed paths but probability clouds, with shapes and energies determined by quantum numbers and interactions.

Orbitals are labeled by the principal quantum number n, the angular momentum quantum number l, and the magnetic quantum number m_l. For a given n, l ranges from 0 to n−1, and the angular part defines the orbital’s shape. S orbitals (l=0) are spherical; p orbitals (l=1) are dumbbell-shaped; d (l=2) and f (l=3) orbitals have more complex forms. The probability density |Ψ|^2 reveals nodal surfaces and regions of high electron density.

In hydrogen-like atoms, energy depends mainly on n; in multi-electron atoms, there is additional splitting by l due to electron–electron repulsion and shielding. Each orbital can hold up to two electrons with opposite spin, in accordance with the Pauli exclusion principle. Subshells defined by n and l (such as 2p or 3d) have fixed capacities determined by the magnetic quantum numbers.

Electron orbitals underpin electron configurations, chemical bonding, and spectroscopic properties. Valence orbitals and their occupancy influence reactivity, while concepts such as orbital hybridization and molecular orbitals describe bonding in molecules. Orbitals are visualizations of probabilistic electron densities and are complemented by computational methods like Hartree–Fock and density functional theory to approximate their shapes and energies.