Quantum Numbers

Quantom numbers are the address of electrons. These are numbers which are used to specify the position and energy of electrons in an atom. Four quantum numbers are usually used to designed the electrons present in an orbital.

Principal Quantum Number ('n')

This represents the main shells in an atom. This number gives the average distance of the electron from the nucleus and hence gives the shell number (i.e. principal energy level) to which the electron belongs. It determines the size energy of orbitals. Thus it gives an idea of the position, of the electron around the nucleus. The energy of the electron depends upon this number. Higher the principal quantum number, greater is its distance from the nucleus, greater is its size and also higher is its energy. It can have any positive value from 1 to infinity. But only values from 1 to 7 have so far been established for atoms of the known elements. Shells are designated as K,L,M,N etc.,when n=1,2,3,4...etc. respectively.

The maximum number of electrons in ‘n’ principal quantum number is given by 2n².

Azimuthal Quantum Number ('l')

This represents the subshell. It determines the shape of orbitals. It also give the orbital angular momentum of an electron and so called angular
 momentum quantum number. It is represented by letter ‘l’.

The value of ‘l’ depends upon the value of principal quantum number ‘n’. For a particular value of ‘n’, the ‘l’ can take the values from 0 to n-1. Each value of ‘l’ represents one particular sub-shell. For example,
For n = 1, n –1 = 0; so, l = 0
For n = 2, n –1 = 1; so, l = 0,1
For n = 3, n –1 = 2; so, l = 0,1, 2
For n = 4, n –1 = 0; so, l = 0,1, 2, 3
The various sub-shells represented by Azimuthal quantum number ‘l’ are s, p, d and f i.e. l = 0, denotes ‘s’ sub-shell, l = 1, denotes ‘p’ sub-shell, l = 2, denotes ‘d’ sub-shell and l = 3, denotes ‘f’ sub-shell. Azimuthal quantum number also gives the angular moment of electron in a particular sub -shell. The angular moment of electron in a particular sub-shell is given by l( l+1) h/2π.

Magnetic Quantum Number ('m')

This represents the orbitals. ie, the orientation of orbitals in sub shells. 'm' can have values from -l to +l including '0'. That is, for an 'l' value , there are  (2l+1) values for 'm'.

(a). If l = 0 (s sub-shell), 'm' will have only one value; m = 0. This means that ‘s’ sub-shell have only one orbital.

(b). If l = 1 (p sub-shell), 'm' will have 3 values; m = – 1, 0 and +1. This means that ‘p’ sub-shell have three orbitals. The three corresponding orbitals are written as px, py and pz.

(c). If l = 2 (d sub-shell), 'm' will have 5 values; m = –2, –1, 0, +1 and +2. This means that ‘d’ sub-shell have five orbitals, represented by dxy, dyz, dzx, dx2-y2 and dz2.

(d). If l = 3 ( f sub-shell), 'm' will have 7 values; m = –3, –2, –1, 0, +1, +2 and +3. This means that ‘f’ sub-shell have seven orbitals.

Spin Quantum Number ('s')

This represents the spin direction of electron. A charged particle which spin about it own axis behaves as a small magnet. Hence spinning of an electron generates a magnetic moment which combines with the magnetic moment generated due to orbital angular momentum of electron. This combination of magnetic moments modifies the energy of the electron in an orbital. Since the electron can spin in clockwise or anti-clockwise directions, the spin quantum number may have two values; +½ and -½. +½ indicates the spinning of electron in clockwise direction and -½ in anti clockwise direction.