Question

What is the Pauli Exclusion Principle, and how does it lead to the conclusion that at most two electrons can occupy an orbital?

Answer 1

In a chemistry based context (i.e. electrons in an atom) Pauli's exclusion principle states that no two electrons in an atom can have all four quantum numbers match.

Explanation:

So even if two electrons are in the same orbital of an atom and so have the same principal quantum number (n), angular momentum quantum number (ℓ), and magnetic quantum number (`m_ℓ`) there magnetic spin state (`m_s`) must be different and so as a result have opposing spin states - +1/2 and -1/2.

This principle outlines why electrons have to occupy differing energy levels - as in, after two electrons have occupied a `1s^2` orbital, a further electron must enter another orbital in order to not violate pauli's exclusion principle.