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Pauli's Exclusion Principle

Hund's Rule
For orbitals having identical energies (degenerate orbitals), electrons with the same spin enter them one by one till all of them are singly occupied. This is followed by the double occupation of these orbitals. Taking an example of 2p orbitals, the order in which the three orbitals are filled up is shown in the following figure. 

The order of filling three p orbitals as required by Hund's rule.

Here, an orbital is represented as a square box and arrows show its occupancy. During the single occupation, the electrons have the same spin (may be a or b). During the double occupation electrons have opposite spin as required by Pauli's principle.
Pauli's Exclusion Principle
Pauli's Exclusion Principle states that no two electrons in the same atom can have the same values for all four quantum numbers. According to this principle, an orbital (known values of n, l and m) can accommodate, at the most, two electrons with opposite spins, since only then will the fourth quantum number ms have different values of + 1/2 and - 1/2, respectively. 
Since within a subshell, 2l + 1 orbitals are possible, the maximum number of electrons that can be accommodated are 2(2l + 1), i.e. 2, 6, 10 and 14 in subshells
s(l = 0), p(l = 1), d(l = 2) and f(l = 3), respectively.

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