sOrbital

sOrbital, or s orbital, is the atomic orbital with angular momentum quantum number l equal to 0, characterized by spherical symmetry. In atoms, electrons occupy orbitals described by the principal quantum number n and l; for sOrbitals, l = 0 and the magnetic quantum number m_l = 0, with two possible spin states. Each sOrbital can hold up to two electrons with opposite spins, in accordance with the Pauli exclusion principle.

In hydrogen-like atoms, the wavefunction for an sOrbital can be written as ψ_{n0m0}(r, θ, φ) = R_{n0}(r) Y_0^0(θ, φ), where Y_0^0 is a constant, yielding a spherically symmetric probability density. The radial part R_{n0}(r) has n−1 radial nodes; the lack of angular nodes reflects its spherical symmetry.

sOrbitals are central to chemical structure and bonding. They are more penetrating near the nucleus than orbitals with higher angular momentum, due to the absence of an angular momentum barrier. This penetration, or orbital screening, influences the effective nuclear charge experienced by electrons. The lowest sOrbital is 1s, followed by 2s, 3s, 4s, and so on. In multi‑electron atoms, orbital energies depend on electron–electron interactions, so the relative ordering of s, p, d, and f orbitals follows the general n + l rule but can vary in practice; a common pattern places 4s before 3d in many ground-state configurations.

sOrbitals play a key role in determining the valence structure of s-block elements (groups 1 and 2) and contribute to chemical properties across the periodic table. Radial electron density, given by 4πr^2|R_{n0}(r)|^2, describes the likelihood of finding an electron at distance r from the nucleus.