Magnetic quantum number and spin

[Freddy86]

Hi, please could someone provide me with an explanation of the differences between the magnetic quantum number and the spin. I thought that the magnetism of an electron/fermion comes from its intrinsic quantum angular momentum (i.e. its quantum spin) which was evidenced by the Stern–Gerlach experiment. So what then does the magnetic quantum number represent and what does it have to do with the magnetic properties of a subatomic particle? Thanks

 

[Nugatory]

Hi, please could someone provide me with an explanation of the differences between the magnetic quantum number and the spin. I thought that the magnetism of an electron/fermion comes from its intrinsic quantum angular momentum (i.e. its quantum spin) which was evidenced by the Stern–Gerlach experiment. So what then does the magnetic quantum number represent and what does it have to do with the magnetic properties of a subatomic particle? Thanks

Spin is the intrinsic angular momentum of the particle while the $m$ quantum number of a bound electron comes from its angular momentum about the nucleus. That angular momentum actually shows up in two of the quantum numbers: $l$ is the quantized magnitude of the "orbital" angular momentum vector, and $m$ is the quantized component of that vector along one axis.

(I put the word "orbital" in scare-quotes, because even though that's what we call we all know that the electron isn't really a little tiny ball going in orbit around the nucleus).

 

[Freddy86]

Spin is the intrinsic angular momentum of the particle while the $m$ quantum number of a bound electron comes from its angular momentum about the nucleus. That angular momentum actually shows up in two of the quantum numbers: $l$ is the quantized magnitude of the "orbital" angular momentum vector, and $m$ is the quantized component of that vector along one axis.

(I put the word "orbital" in scare-quotes, because even though that's what we call we all know that the electron isn't really a little tiny ball going in orbit around the nucleus).

Thanks for your reply. So I just found a really good video about magnetism in an atom () which says there is a contribution from the angular momentum about the nucleus (although it usually cancels out) and an intrinsic angular momentum (spin). So when people talk about the magnetism that comes form the angular momentum about the nucleus are they explicitly referring to magnetic quantum number (m).

 

[Nugatory]

So when people talk about the magnetism that comes from the angular momentum about the nucleus are they explicitly referring to magnetic quantum number (m).

Generally, yes... But don't confuse that with the (much smaller) magnetic moment of the nucleus itself, and be careful about the context, as people aren't always consistent and careful in their use of words.