Concept Summary
Atomic Orbitals and Quantum Numbers
Molecular Orbitals
Hybridization
Quantum numbers describe the size, shape, orientation, and number of atomic orbitals an
element possesses.
The principal quantum number, n, describes the energy level (shell) in which an electron resides
and indicates the distance from the nucleus to the electron. Its possible values range from 1 to ∞.
The azimuthal quantum number, l, determines the subshell in which an electron resides. Its
possible values range from 0 to n – 1. The subshell is often indicated with a letter: l = 0
corresponds to s, 1 is p, 2 is d, and 3 is f.
The magnetic quantum number, ml, determines the orbital in which an electron resides. Its
possible values range from –l to +l. Different orbitals have different shapes: s-orbitals are
spherical, while p-orbitals are dumbbell-shaped and located on the x-, y-, or z-axis.
The spin quantum number, ms, describes the spin of an electron. Its possible values are
Bonding orbitals are created by head-to-head or tail-to-tail overlap of atomic orbitals of the
same sign and are energetically favorable.
Antibonding orbitals are created by head-to-head or tail-to-tail overlap of atomic orbitals that
have opposite signs and are energetically unfavorable.
Single bonds are sigma (σ) bonds, which contain two electrons.
Double bonds contain one σ bond and one pi (π) bond. π bonds are created by sharing of
electrons between two unhybridized p-orbitals that align side-by-side.
Triple bonds contain one σ bond and two π bonds.
Multiple bonds are less flexible than single bonds because rotation is not permitted in the
presence of a π bond. Multiple bonds are shorter and stronger than single bonds, although
individual π bonds are weaker than σ bonds.
