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The Pauli exclusion principle is the quantum mechanicalprinciple that states that two or moreidenticalfermions(particles with half-integerspin) cannot occupy the samequantum statewithin aquantum system simultaneously.

Given that the atomic number of oxygen is Z(O) = 8

The atomic number of nitrogen is Z (n) =7

The electron configuration for oxygen is${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{4}}$

The electron configuration for nitrogen is$1s^{2}2s^{2}2p^3$

For nitrogen, the three electrons in the 2p shell ( I = 1) can all be in a different spatial state, since the possible values for m₁ are -1, 0, and 1. Unlike nitrogen, the oxygen atom has 4 electrons in the 2p shell. Again, the quantum number can have possible values of -1, 0, or 1. Since there are 4 electrons present, this means that two of them must be in the same spatial state. This increases the energy since there is repulsion between the two electrons and thus it is slightly easier to 'take' a 2p electron from oxygen that in it is from nitrogen. In other words, the first ionization energy is slightly smaller for oxygen than it is for nitrogen.

Therefore two of the 2p oxygen electrons must be in the same spatial state due to the Pauli exclusion principle.