Question

This is a very simple question. Today, someone explained to me that the Pauli exclusion principle says that no two electrons can occupy the same energy state. However, I believe that this language is not precise as two electrons can occupy the same energy state, allowing they have different spin. Rather it is the quantum state that cannot be the same.

So, my question is, is it wrong to say energy state?

Answer 1

The Pauli exclusion principle states that no two electrons can have the same quantum state rather than just the same energy level. While electrons can share the same energy level, their spin quantum numbers must be different for them to comply with this principle.

Step-by-step explanation:

The proper way to express Wolfgang Pauli's 1925 principle in physics is that no two electrons can occupy the same quantum state within an atom. The confusion arises from the term 'energy state', which often refers to the principal quantum number 'n' indicating the electron's energy level. However, each energy level contains multiple sublevels and orbitals, where the electrons can differ in their quantum numbers. The Pauli exclusion principle is more precisely focused on the overall quantum state, which includes four quantum numbers (n, l, ml, and ms) that describe not only the energy level but also the orbital shape, orientation, and spin of the electron. Two electrons occupying the same orbital can indeed have the same energy level, but one will have an up spin while the other has a down spin; thus, they have different spin quantum numbers (ms).