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I'm having a bit of a hard time imagining the 3 dimensional structure of the atom and its orbitals. So here's what I know/think: The nucleus is in the center, and as n increases so does the distance from the radius. At these distances n=1, n=2, and so on, there are certain shapes/orbitals that get increasingly further from the nucleus (so in a sense they repeat with increasing n with the addition of another shape). Not all these shapes have symmetry I think. Do these shapes exist with respect to the nucleus as the center of the shape? Any help/elaboration would be much appreciated. Thanks.
A lot of your thinking is spot on! One thing you might want to clarify is your comment about symmetry. All of the orbitals have some sort of symmetry, but I think what you were referring to was the idea the the s sub shell has spherical symmetry, therefore it can't have any other orientations. This is not the case for p or d orbitals (although they are symmetric, just not the same kind of symmetry as an s orbital) and so they have different orientations in relation to the nucleus. However the orientations does nothing to the energy level of the orbital, which is what we call degenerate orbitals.
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