Orbitál

Orbitál, in chemistry and atomic physics, is a mathematical function that describes the region of space where there is a high probability of finding an electron in an atom. Orbitals arise as solutions to the Schrödinger equation for electrons moving in the Coulomb field of the nucleus and are labeled by quantum numbers that encode their energy and shape.

The principal quantum number n indicates the energy level, while the angular momentum quantum number l (ranging from 0 to n−1) determines the orbital type: s (l = 0), p (l = 1), d (l = 2), and f (l = 3) as the common categories. The magnetic quantum number m_l, which runs from −l to +l, describes the orientation of the orbital in space, and the spin quantum number m_s takes values of ±1/2 for each electron. An orbital can hold up to two electrons with opposite spins, in line with the Pauli exclusion principle. Subshells are grouped into shells by the principal quantum number and are denoted by the corresponding letter and number (for example, 2p, 3d).

Orbitals describe electron density distributions rather than fixed paths. Their shapes vary: s orbitals are spherical, p orbitals have a dumbbell shape, while d and f orbitals possess more complex geometries. The arrangement of electrons into orbitals (and their occupancy rules, such as Hund’s rule) underpins the chemical properties of elements, bonding, and molecular structure. In molecules, atomic orbitals combine to form molecular orbitals, which determine bond strength and reactivity. The concept of orbitals remains central to quantum chemistry and atomic physics.