Spin Quantum Number $(m_s)$:$m_s=+\frac{1}{2}$ or $-\frac{1}{2}.$

Specifies the orientation of the spin axis of an electron. An electron can spin in only one of two directions $($sometimes called up and down$).$

The Pauli exclusion principle $($Wolfgang Pauli, Nobel Prize $1945)$ states that no two electrons in the same atom can have identical values for all four of their quantum numbers. What this means is that no more than two electrons can occupy the same orbital, and that two electrons in the same orbital must have opposite spins.

Because an electron spins, it creates a magnetic field, which can be oriented in one of two directions. For two electrons in the same orbital, the spins must be opposite to each other; the spins are said to be paired. These substances are not attracted to magnets and are said to be diamagnetic. Atoms with more electrons that spin in one direction than another contain unpaired electrons. These substances are weakly attracted to magnets and are said to be paramagnetic.

Table of Allowed Quantum Numbers

$\backslash$table$[[n,\frac{1}{2},\frac{m_L}{0},\backslash$table$[[$Number of$],[$orbitals$]],\backslash$table$[[$Orbital$],[$Name$]],\backslash$table$[[$Number of$],[$electrons$]]],[2,0,0,1,1s,2],[,0,0,1,2s,2],[1,-1,0,+1,3,2p,6,]]$

$3$

$4$

$5$