1sorbital

The 1s orbital is the lowest-energy atomic orbital, designated by the principal quantum number n = 1 and the azimuthal quantum number l = 0. It is spherically symmetric and can hold up to two electrons with opposite spins. As the innermost electron shell, the 1s orbital plays a central role in shaping the electronic structure of atoms and the overall shielding of outer electrons.

In hydrogen-like atoms, the 1s wavefunction has an explicit form: ψ_1s(r) = (Z^3/π a0^3)^{1/2} e^{-Z r / a0}, where Z is the nuclear charge and a0 is the Bohr radius. The electron density, given by |ψ_1s(r)|^2, decays exponentially with distance from the nucleus. The 1s orbital has no angular nodes and, for n = 1, no radial nodes either; the radial distribution peaks near the nucleus and diminishes rapidly with r.

In multi-electron atoms, the 1s orbital remains the innermost shell and is subject to screening by other electrons. Its effective binding is characterized by an effective nuclear charge Z_eff, making it more contracted as Z increases. The 1s electrons are highly bound and typically contribute to core properties rather than chemical bonding, though they influence elemental shielding, ionization energies, and X-ray spectra.

Notation-wise, the 1s orbital is often denoted as 1s, and its two-electron occupation is written as 1s^2 for atoms whose ground state includes a filled 1s shell. The concept of the 1s orbital is fundamental to discussions of atomic structure, spectroscopy, and quantum chemistry.