Significance of Quantum Numbers

The three quantum numbers describe the size, shape, and orientation of the atomic orbitals in space. There is an additional quantum number which does not follow from the Schrödinger wave equation but is introduced to account for electron spin.

Principal Quantum Number

The principal quantum number, n describes the energy level (or principal shell) of the electron within the atom. n can have only positive non-zero integral values (n = 1,2,3,4…). This means that in an atom, the electron can have only certain energies.

The principal quantum number also determines the mean distance of the electron from the nucleus (size). Greater the value of n farther is the electron from the nucleus.

Each principal shell can accommodate a maximum of 2n2 electrons.

  • n = 1, number of electrons: 2
  • n = 2, number of electrons: 8
  • n = 3, number of electrons: 18
  • n = 4, number of electrons: 32

Azimuthal Quantum Number

The azimuthal quantum number, l is related to the geometrical shape of the orbital. The value of l may be zero or a positive integer less than or equal to n–1 (n is the principal quantum number).

l = 0,1,2,3, …,(n–1).

Different values of l correspond to different types of subshells and each subshell contains orbitals of a given shape.

  • l = 0, corresponds to s-subshell and contains the orbital with spherical shape called as s orbital.
  • l = 1, corresponds to p-subshell and contains the orbitals with a dumb-bell shape called as p-orbitals. There are three p-orbitals in each p-subshell.
  • l = 2, corresponds to d-subshell and contains the orbitals with a cloverleaf shape called as d-orbitals.
  • l = 3, corresponds to f-subshell and contain f orbitals. There are seven f-orbitals in each f-subshell.

Magnetic Spin Quantum Number

The quantum number, ms, describes the spin of the electron - whether it is clockwise or anticlockwise. The quantum number does not arise while solving SWE. The clockwise and anticlockwise direction of electron spin has arbitrarily been assigned the values as +½ and –½ respectively.