# What is the maximum number of electrons that can occupy an orbital if they have different spins?

##### 1 Answer

This follows directly from the **Pauli Exclusion Principle**, which states that *no two electrons can share the same quantum state.* This means that no two electrons can have the same quantum numbers

#n# is the**principal quantum number**, usually indicating what atomic energy level we are in.#l# is the**angular momentum quantum number**, corresponding to the shape of the orbital. It defines the orbital subshell.#m_l# is the**magnetic quantum number**, corresponding to each particular orbital in a given subshell defined by#l# .#m_s = pm1/2# is the**electron spin quantum number**, where#+# indicates spin-up (and thus of course,#-# indicates spin-down).

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A particular orbital therefore has a single *any electron in a specific orbital* already shares *three of four* quantum numbers.

It follows that when electrons have **two** different spins in a particular orbital (and there exist only two spins for the electron!), these **two** electrons have occupied all the allowed quantum states within that orbital.