Question

State and explain Pauli’s exclusion principle.

Answer 1

Pauli’s exclusion principle:

1. Statement: “No two electrons in an atom can have the same set of four quantum numbers”. OR “Only two electrons can occupy the same orbital and they must have opposite spins.”
2. The capacity of an orbital to accommodate electrons is decided by Pauli’s exclusion principle.
3. According to this principle, for an electron belonging to the same orbital, the spin quantum number must be different since the other three quantum numbers are the same.
4. The spin quantum number can have two values: `+1/2` and `-1/2`.
5. For example, consider helium (He) atom with electronic configuration 1s².
   For the two electrons in 1s orbital, the four quantum numbers are as follows:
   

   Electron number	Quantum number				Set of values of quantum numbers
   	n	l	m	s
   1st Electron	1	0	0	`+1/2`	`(1,0,0,+1/2)`
   2nd Electron	1	0	0	`-1/2`	`(1,0,0,-1/2)`

   Thus, in an atom, any two electrons can have the same three quantum numbers, but the fourth quantum number must be different.
6. This leads to the conclusion that an orbital can accommodate a maximum of two electrons and if it has two electrons, they must have opposite spin.