Four quantum numbers are required to understand the location and energy of each electron in an atom. They are:

Principal quantum number (n)

This number represents the average distance of an electron from the nucleus and corresponds to the principal energy level in which the electron resides. The allowed values of this quantum number are n = 1, 2, 3, & & & & . The principal energy levels or shells having different values of n are also represented by K, L, M, N and so on. The maximum number of electrons that can occupy a shell corresponding to the principal quantum number 'n' is 2n².

Another name for this quantum number is orbital angular momentum quantum number. This quantum number gives the measure of the angular momentum of an electron in its orbit. Physically, this number indicates the shape of the classical orbit. For a given value of 'n', 'l' can take all positive integral values from 0 to (n-1). The subshells with l = 0,1,2, & & & . are designated s, p, d, f, g, h, k, & & & respectively. For a given 'n' the energies of various subshells are in the order s<p<d<f & & & . The magnitude of the angular momentum is given by the equation

hÖl (l+1) / 2p

Magnetic quantum number ( m_L )

The magnetic moment of an electron due to its orbital motion gives rise to a magnetic field which can interact with an external magnetic field. The electron orient themselves in certain preferred regions of the space around the nucleus under the influence of an external magnetic field. The preferred orientation of the orbitals in space is determined by the magnetic quantum number m₁. This is with respect to an applied magnetic field.

The total allowed possible values of

l can take on the value 0. The magnitude of angular momentum's components along the direction of the magnetic field is

Spin Quantum number ( m₂ )

An electron spins and this results in two spin states i.e., in a magnetic moment which can be either parallel or antiparallel to the surrounding magnetic field. The only two possible values for m₂ are +1/2 or - 1/2.

These quantum numbers i.e., n₁, l₁, m₁ & m₂ determine together the position of an electron in an atom. No two electrons in an atom have the same value for all the 4 quantum numbers. This is 'Pauli's Exclusion Principle' Electrons who have the same value for n constitute a shell. A shell can have a maximum of 2n electrons.