This Demonstration shows an implementation of P. A. M. Dirac's prophecy: "Chemistry will become an exercise of applied math".

The configuration of the atom is determined by a set of orbital quantum numbers: principal , orbital angular momentum and spin magnetic . For each energy level , there are orbitals divided into subshells, depending on , the second quantum number. Also a third quantum number can be found, and the triplets are shown on the bottom. A letter code is used to classify each subshell: an subshell corresponds to , a subshell to , a subshell to and an subshell to [1].

Select "quantum numbers" to show the triplets for the first four energy levels .

Select "atomic orbitals" to show the explicit form of the orbitals.

Select "radial distribution function" to show the probability distribution of each orbital. The energy of each subshell varies with [1].

Select "cumulative radial distribution function" to show the cumulative probability distribution of each orbital.

Snapshot 1: orbital quantum numbers: principal (), orbital angular momentum () and spin magnetic (); the sum of the odd numbers of each subshell is equal to

Snapshot 2: orbital shapes with

Snapshot 3: radial probability of each orbital with

Snapshot 4: cumulative radial probability of each orbital with ; each cumulative probability tends to 1 as every single probability is normalized