Pauli Exclusion Principle is a very important principle in quantum chemistry and physics. According to the current generally accepted atomic model each electron possesses four quantum numbers. Pauli Exclusion Principle states that in an atom there cannot be two electrons that have the same four quantum numbers.
In order to explain Pauli Exclusion Principle, we first have to explain how the four quantum numbers of an electron work and what is their meaning. The principal quantum number (n) describes the energy level at which the electron is located in the atom orbitals. The angular momentum quantum number (l) describes the shape and the angular distribution of the orbital where the electron is located. Therefore, the second quantum number indicates the subshell (an orbital with an specific shape) where the electron is located. The magnetic quantum number (ml) indicates the orientation in the space of the orbital where the electron is located. Lastly, the spin quantum number (ms) indicates the direction of the electron spin around the orbital. In this case there are only two option for any electron, +1/2 or -1/2.
According the Exclusion Principle, if two electrons have the same first three quantum numbers (n, l, ms), they must have different spin quantum number: one of the electrons must have +1/2 and the other one -1/2.
In order to represent this principle theoretically, the electrons of a same energy level, same shell and same orbital orientation must be represented as shown below:
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