# How can an electron shell hold more than two electrons?

The Pauli Exclusion principle states

in an atom or molecule, no two electrons can have the same four electronic quantum numbers. As an orbital can contain a maximum of only two electrons, the two electrons must have opposing spins.

So how can some electron shells have up to 6 electrons or more? Take the electron configuration of Magnesium. The 2p shell holds 6 electrons. How is this possible? Can you have multiple orbitals in a single electron shell?

• Comments are not for extended discussion; this conversation has been moved to chat. – David Z Aug 16 '16 at 14:56

A "shell" is the term for all states with the same principal quantum number $n$, but in each shell there are also possible different values for the angular momentum quantum number $0\leq \ell \leq n$, the magnetic quantum number $-\ell \leq m_\ell \leq \ell$ and the spin quantum number $m_s\in\{-1/2,1/2\}$.
So for $n>1$, 6 electrons in a shell do not violate the Pauli exclusion principle.
• Note that the OP seems to be using "shell" to mean definite $n$ and $\ell$, since they talk about the "2p shell". (I think most sources would call this a "subshell" instead.) Your logic is still fine for any subshell with $\ell \neq 0$, though. – Michael Seifert Aug 15 '16 at 19:40