Quantum number

A quantum number is one of a set of discrete values that label the allowed states of a quantum system, such as an electron bound in an atom. Because bound quantum systems can occupy only certain states, each state is identified by integers or half-integers rather than a continuous range. For the hydrogen atom, four quantum numbers specify an electron's state.

#The atomic quantum numbers

The principal quantum number n sets the energy level and shell; the azimuthal number l sets the orbital shape and angular momentum; the magnetic number m sets the orientation in a field; and the Spin quantum number distinguishes the two spin orientations of the electron. The Pauli exclusion principle forbids two electrons in an atom from sharing all four values, which gives atoms their shell structure and underlies the periodic table. Together the quantum numbers form a compact description of a quantum state for such systems.