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I was hoping that someone would be able to clarify what l and ml actually represent. I understand that l distinguishes the shape of the orbital and ml indicates the orientation of the orbital. However, I'm confused because on page 35 of the textbook it says, "As its name suggests, l tells us the orbital angular momentum of the electron, a measure of the rate at which (in classical terms) the electron "circulates" round the nucleus." Then on page 36 it says, "The magnetic quantum number tells us the orientation of the orbital motion of the electron. Specifically, it tells us that the orbital angular momentum around an arbitrary axis is equal to mlh." I'm confused because these two statements are very similar but are describing different quantum numbers. It seems that the book is saying that both l and ml describe the momentum of the electron. If someone could explain the difference to me I would appreciate it.
So l is the momentum of the electron rotating around the nucleus. Ml on the other hand, is the angle at which the electron is rotating around the nucleus. If you look at orbitals and their different shapes, you'll see that each ml has a different orbital shape and this ml number determines exactly where the orbitals are in space.
In layman terms, l essentially tells us the speed of the electron's rotation around the nucleus, and ml tells us the orientation/ angle of this rotation.
The quantum number l is the orbital angular momentum of the electron. It is the rate that the electron rotated round the nucleus and the shape. The magnetic quantum number ml specifies the orbitals of the subshell and the orientation.
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