Q.State the Pauli exclusion principle and give one direct consequence it has for the maximum number of electrons an orbital can hold.

Statement. The Pauli exclusion principle (Wolfgang Pauli, 1925) states that no two electrons in the same atom can possess an identical set of all four quantum numbers ($n$, $l$, $m_l$, $m_s$).

Consequence for orbital capacity. Since $n$, $l$ and $m_l$ together already specify one particular orbital, two electrons occupying the same orbital necessarily share the same values of $n$, $l$ and $m_l$. For these two electrons to still have different complete sets of quantum numbers (as the principle requires), they must differ in their fourth quantum number, $m_s$. Since $m_s$ can only take one of two values, $+\tfrac{1}{2}$ or $-\tfrac{1}{2}$, at most two electrons can occupy any one orbital, and if it holds two, they must have opposite (paired) spins -- one $+\tfrac{1}{2}$ and one $-\tfrac{1}{2}$. A third electron in that same orbital would be forced to repeat a spin value already used, …

State the principle directly, then reason from it: since an orbital fixes $n$, $l$, $m_l$, and $m_s$ has only two allowed values, at most …

Stating the principle only in words without connecting it to WHY it limits orbital occupancy to two; forgetting that the two electrons i …