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does m tell us anything about the magnetic properties of the system since it is called magnetic quantum number? and if it does, what information exactly does it give us regarding magnetic properties?
<math>m</math> refers to the orientation of particular orbitals in each subshell. I believe <math>m</math> is called the magnetic quantum number because the effect of the different orbital positions were first studied through the Zeeman effect, the splitting of a spectral line when in the presence of a static magnetic field.
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