sOrbitals

S orbitals are atomic orbitals characterized by an azimuthal quantum number l equal to 0, which gives them spherical symmetry. In the quantum-mechanical description of electrons in atoms, orbitals are described by wavefunctions that separate into a radial part and an angular part. For s orbitals the angular part is constant (the spherical harmonic with l = 0), so the electron probability density depends only on the distance from the nucleus.

Each s orbital is labeled by a principal quantum number n (n = 1, 2, 3, …). The radial distribution function Rn0(r) governs how the electron density varies with distance from the nucleus. The 1s orbital has no radial nodes and is strongly peaked at the nucleus, while higher s orbitals (2s, 3s, …) have one or more radial nodes where the density falls to zero. Across the series, the overall density becomes more spread out but remains spherical.

In hydrogen-like atoms, energy depends only on n, so all s orbitals with the same n are degenerate. In multi-electron atoms, shielding and penetration lift this degeneracy; s orbitals are highly penetrating and lie closer to the nucleus than orbitals of higher angular momentum with the same principal quantum number. This penetration affects chemical behavior, including shielding of inner electrons and effective nuclear charge felt by valence electrons.

Chemically, s orbitals participate in bonding and hybridization. Valence electrons often occupy outer s and p orbitals and can form sigma bonds or hybrid orbitals (such as sp, sp2, sp3) that accommodate bonding and molecular geometry. Examples include the 1s orbital in hydrogen and the 2s orbital in carbon and oxygen.