s, p, d, f orbitals

The letters s, p, d, and f name the different types of atomic orbital, classified by the orbital's angular momentum — the quantum number ℓ. An s orbital has ℓ equal to zero and is perfectly round, a single ball of probability centred on the nucleus. A p orbital has ℓ equal to one and forms a dumbbell with two lobes; d and f orbitals, with ℓ of two and three, take on progressively more elaborate cloverleaf and multi-lobed shapes.

The labels are historical, drawn from old descriptions of spectral lines — sharp, principal, diffuse, and fundamental — but they have stuck as the standard vocabulary of chemistry. Within a shell, each type forms a subshell: there is one s orbital, three p orbitals pointing along the three axes, five d orbitals, and seven f orbitals, the count rising as two times ℓ plus one. Each individual orbital still holds at most two electrons.

These shapes are the reason chemistry looks the way it does. The round s orbitals and directional p orbitals govern the bonds of the everyday elements, while the d orbitals give the transition metals their colours and catalytic powers and the f orbitals shape the rare-earth elements. Knowing which subshell an atom's outermost electrons live in tells you most of what you need to predict how it will react.