State and explain Pauli's Exclusion Principle.

Pauli’s Exclusion Principle: It states: No two electrons in an atom can have the same set of all the four quantum numbers (n, l, m, s).
According to this principle, two electrons in an atom can have a maximum of three quantum numbers identical but the value of the fourth quantum number must be different. Electrons having the same set of values n, l and m are said to belong to the same orbital.
For example, for K shell i.e. when n = 1

Thus, we conclude from the above that:
(i) an orbital cannot have more than 2 electrons, (ii) if an orbital has two electrons, they must have opposite spin.
Application of Pauli’s Exclusion Principle: The maximum number of electrons in different sub-shells and energy levels can be deduced from this principle.
For L shell (n = 2)

n	l	m	s
2 2 2 2 2 2 2 2	0 0 1 1 1 1 1 1	0 0 -1 -1 0 0 +1 +1	+1/2 -1/2 +1/2 +1/2 -1/2 -1/2 +1/2 -1/2

The second energy level (L-shell) can contain maximum 8 electrons. 
2 in l = 0 i.e. s-subshell
6 in l = 1 i.e. p-subshell
Similarly, it can be easily shown that third energy level (M shell) can contain maximum 18 electrons.
2 in  s subshell
6 in p subshell
10 in d subshell
Similarly, it can be easily shown that fourth energy level (N shell) can contain maximum 32 electrons.
2 in s subshell
6 in p subshell
10 in d subshell
14 in f subshell