What Is the Role of Angular Momentum in Electron Behavior Within Atoms?

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Angular momentum plays a crucial role in describing electron behavior within atoms, characterized by energy levels, orbital shapes, orientations, and spin. The energy level (n) influences the electron's average distance from the nucleus, while the shape (l) defines the orbital's geometry. The magnetic moment (m_l) determines the orientation of these orbitals, which can vary based on the electron's environment. Although electrons exhibit properties akin to spinning, the concept of actual rotation is less significant than their interactions that mimic spin behavior. Ultimately, the definition of "up" or "down" in terms of spin is context-dependent, particularly when electrons are bound within an atom.
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I'm reading about properties of electrons in atoms, and it says an electron's position in an atom can be described by energy level, shape, orientation, and spin
roughly speaking:
the energy level (n) dictates the radius from the nucleus (probability wise)
the shape (l) dictates... the shape of the orbital
the magnetic moment (m_l) dictates the way that shape is oriented (relative to what set of coordinates? I mean "down" isn't towards the center of the earth, I imagine)
and spin, which dictates... what the electron does when passed through a magnetic field?
a charge that spins generates a magnetic field?
the the electron actually rotating about a center axis?

thanks!
 
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Electrons appear to possesses angular momentum. Whether or not that means that they actually 'spin' is not particularly relevant or meaningful. They interact with other things as if they do spin.

Although, to respond to the detail in your OP about what is 'up' or 'down'. The spinning of the electron seems to depend upon its environment so I guess you could say that it is only 'spinning' when it is actually in an atom and an axis can be defined. That's when the +/-1/2 quantum numbers come into describe the spin. A free electron may behave differently and I'm not sure whether they can be sorted into + and - spin piles. After all, up/down/left/right are not fundamental to an electron that's just hanging there.
 
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