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Fixed quantum angular momentum in a given direction.
Can range between .
E.g. consider gallium which is 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p1:
  • the electrons in s-orbitals such as 1s, 2d, and 3d are , and so the only value for is 0
  • the electrons in p-orbitals such as 2p, 3p and 4p are , and so the possible values for are -1, 0 and 1
  • the electrons in d-orbitals such as 2d are , and so the possible values for are -2, -1, 0 and 1 and 2
The z component of the quantum angular momentum is simply:
so e.g. again for gallium:
  • s-orbitals: necessarily have 0 z angular momentum
  • p-orbitals: have either 0, or z angular momentum
Note that this direction is arbitrary, since for a fixed azimuthal quantum number (and therefore fixed total angular momentum), we can only know one direction for sure. is normally used by convention.


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