Editing Quantum number (section)

=== Spin magnetic quantum number ===
The [[spin magnetic quantum number]] describes the intrinsic [[Spin (physics)|spin angular momentum]] of the electron within each orbital and gives the projection of the spin angular momentum {{mvar|S}} along the specified axis:

<math display=block>S_z = m_s \hbar</math>

In general, the values of {{mvar|m<sub>s</sub>}} range from {{math|−''s''}} to {{mvar|s}}, where {{mvar|s}} is the spin quantum number, associated with the magnitude of particle's intrinsic spin angular momentum:<ref>{{cite book|title=Quantum Mechanics |edition=2nd |first1=Y. |last1=Peleg |first2=R. |last2=Pnini |first3=E. |last3=Zaarur |first4=E. |last4=Hecht |series=Schuam's Outlines |publisher=McGraw Hill (USA) |date=2010 |isbn=978-0-07-162358-2}}{{page needed|date=February 2019}}</ref>

<math display=block>m_s = -s, -s+1, -s+2, \cdots, s-2, s-1, s</math>

An electron state has spin number {{math|1=''s'' = {{sfrac|1|2}}}}, consequently {{mvar|m<sub>s</sub>}} will be +{{sfrac|1|2}} ("spin up") or −{{sfrac|1|2}} "spin down" states. Since electron are [[fermions]] they obey the [[Pauli exclusion principle]]: each electron state must have different quantum numbers.  Therefore, every orbital will be occupied with at most two electrons, one for each spin state.