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# Pauli's exclusion principle and Uses

The filling of electron into the orbitals of different atoms takes place according to the Aufbau principle, which is based on the Pauli's exclusion principle and the Hund's rule of maximum multiplicity.

Pauli's exclusion principle and Uses

The filling of electron into the orbitals of different atoms takes place according to the Aufbau principle, which is based on the Pauli's exclusion principle and the Hund's rule of maximum multiplicity.

The distribution of quantum numbers among the electrons in a given atom is governed by Pauli's Exclusion principle, which states that 'it is impossible for any two electrons in a given atom to have all the four quantum numbers identical' i.e., in an atom, two electrons can have maximum three quantum numbers (n, l and m) the same and the fourth (s) will definitely be having a different value. Thus if s = +1/2 for one electron, s should be equal to -1/2 for the other electron. In other words the two electrons in the same orbital should have opposite spins (-�).

Uses of the principle

The greatest use of the principle is that it is helpful in determining the maximum number of electrons that a main energy level can have. Let us illustrate this point by considering K and L shells.

K-shell: For this shell n = 1. For n = 1, l = 0 and m = 0. Hence s can have a value either +1/2 or -1/2. The different values of n, l, m and s given above give the following two combinations of the four quantum numbers, keeping in view the exclusion principle. Combination (i) is for one electron and combination (ii) is for the other electron.
n = 1, l = 0, m = 0
s = +1/2 (1st electron)

n = 1, l = 0, m = 0,
s = -1/2 (2nd electron)
(Two electrons in l = 0 sub-shell i.e., 1s-orbital)

These two combinations show that in K shell there is only one sub-shell corresponding to l = 0 value (s-sub-shell) contains only two electrons with opposite spins.

L-shell: For this shell n = 2. For n = 2 the different values of l, m and s give the following eight combinations of four quantum numbers.

n= 2, l = 0, m = 0, s = +1/2

n = 2, l = 0, m = 0, s = -1/2

n = 2, l = 1, m = 0, s = +1/2

n = 2, l = 1, m = 0, s = -1/2

n = 2, l = 1, m = +1, s =  +1/2

n = 2, l = 1, m = +1, s =  -1/2

n = 2, l = 1, m = -1, s =  +1/2

n = 2, l = 1, m = -1, s =  -1/2

Eight combinations given above show that L shell is divided into two sub-shells corresponding to l = 0 (s sub-shell) and l = 1 (p sub-shell) and this shell cannot contain more than 8 electrons, i.e., its maximum capacity for keeping the electrons is eight.

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