Quantum numbers are supposed to denote every individual orbital. But if orbital shells are probability functions, then orbitals can't be definite, solid things. So in that case, there can be variation in the amount of energy given off when an electron drops between shells - it might, say, give off a tiny little bit more energy and drop to just below the orbital shell. Isn't this possible since orbitals are just probability functions - like "Here's where the electron probably is"? Not entirely sure where I was going with this, but I think the final question is, how come quantum numbers are only ever integers?
Edit: My question is about why quantum numbers as taught in schools are always integers. "Orbitals" as predicted by the Bohr model are in fact clouds of electrons, probability functions about where an electron probably is rather than a definite statement about where it definitely is. That means there's got to be wiggle room about how far an electron can be from the nucleus.
So does that mean that quantum numbers are an oversimplification, or just averages? Or am I just misunderstanding the whole "orbitals are just probability clouds" thing?
Edit: Ugh. Right. I'm an idiot. I forgot to mention that I'm only talking about the principal quantum number, n, the one telling which orbital the electron's in.