Why are do some electron orbitals have a negative number in the subscript (i.e. f-1), some a positive (f1), and some have a 0 (f0)? What do these numbers tell you about the atom? I know that these orbitals have different shapes, but I was wondering if they had any other effect on the atom/ion and if there was a reason that they were put in the order that they are in now.
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There are no such things as positive or negative electron orbitals. The number in the subscript is $m$, known as magnetic quantum number and running from $−\ell$ to $\ell$. It doesn't tell you much about the atom. It is a property of the orbital, not of the atom. Every atom has all these orbitals at once (some of them occupied and some empty); also, there are versions of each for different $n$.
In a free atom, all orbitals with the same $n,\;\ell$ and different $m$ have the same energy, so this number does not mean much for an orbital either (at least unless you put the atom in a magnetic field).
Moreover, the pictures are fake anyway. Orbitals which are the true eigenfunctions of $m$ (that is, correspond to specific $m$) are complex-valued and thus can't be properly represented in a plot. As for the orbitals featured on this diagram (and all over the textbooks), these are the linear combinations of complex orbitals for different $m$, hence each of them does not correspond to any particular $m$. It's not that they are wrong per se (absolutely not!), it's just that you can't point at them and tell which is $p_1$ and which is $p_{-1}$.
answered Apr 11, 2016 at 13:27