Pauli Exclusion Principle

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The Pauli Exclusion Principle states that, in an atom, no two electrons can have the same four electronic quantum numbers. We are aware that in one orbital a maximum of two electrons can be found and the two electrons must have opposing spins. That means one would spin up ( +1/2) and the other would spin down (-1/2).

We have the first three quantum numbers \(n=1\), \(l=0\), \(m_l=0\). Only two electrons can correspond to these, which would be either \(m_s = -1/2\) or \(m_s = +1/2\). As we already know from our studies of quantum numbers and electron orbitals, we can conclude that these four quantum numbers refer to 1s subshell. If only one of the \(m_s\) values is given then we would have 1s1 (denoting Hydrogen) if both are given we would have 1s2(denoting Helium). Visually this would be represented as:

As you can see, the 1s subshell can hold only two electrons and when filled the electrons have opposite spins.