Pauli Exclusion Principle is the quantum mechanical principle which states that two or more identicalfermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously
Particles with an integer spin, or bosons, are not subject to the Pauli exclusion principle: any number of identical bosons can occupy the same quantum state
Electrons
In the case of electrons in atoms, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers:
- n - the principal quantum number
- ℓ - the azimuthal quantum number
- mℓ- the magnetic quantum number
- ms- the spin quantum number
For example, if two electrons reside in the same orbital, then their n, ℓ, and mℓ values are the same, therefore their ms must be different, and thus the electrons must have opposite half-integer spin projections of 1/2 and −1/2