Atomic Orbital
A mathematical function describing the three-dimensional spatial wave function and probability distribution of an electron in an atom.
Governing formula
ψ_n,l,m_l(r, θ, φ) = R_n,l(r) Y_l,m_l(θ, φ)
SI unit
Dimensionless Spatial Function
In depth
Atomic orbitals are characterized by three quantum numbers (n, l, m_l). Their shapes represent spatial regions where electron probability density is highest: s-orbitals are spherical (l=0), p-orbitals are dumbbell-shaped (l=1), and d-orbitals are cloverleaf-shaped (l=2).
Examples in the real world
Spherical 1s orbitals forming chemical sigma bonds, and directional 2p orbitals forming pi bonds in molecular chemistry.