Q1.
I understand that every atomic orbital can be uniquely defined by a set of three quantum numbers. The magnetic quantum number distinguishes orbitals with given n and l, which have different orientations in space. For example, a p-orbital can have three possible orientations in space, each, as the internet reveals, denoted by p_x, p_y and p_z. I'm fine with that, but when you get to orbitals of d-orbitals and f-orbitals, the subscripts become awfully complex. What I want to know is: how were the subscripts determined? Is there some sort of way in which one can derive each subscript from scratch?
Ultimately the simple answer is just that they "fall out" of the Schrodinger equation. You solve the Schrodinger equation for those particular orbitals, and mapping those solutions will give you the shape of that orbital*; the "subscripts" are then assigned in accordance with the orientations of those 'shapes' with respect to each other using common sense.
So, for example, three of the solutions for d orbitals of any given n value look exactly the same, but are oriented in different 2D planes of space all orthogonal to each other. It therefore makes sense to call these the d
xy, d
xz and d
yz orbitals. The same ideas apply to the more 'complicated' subscripts as well, although I imagine there are more formal rules for their determination...
You really don't need to worry about any of this
at all for VCE though!
(*orbitals don't actually have boundaries, so the "shapes" you see are (usually) the region of space within which the electron will be found
90% of the time)
Q2.
What is meant by 'formal charge'?
Thanks!
"Formal charge" is just the charge on an atom in a molecule if you assume that the electrons in any covalent bond are shared equally between both participating atoms (i.e. one each and ignoring differences in electronegativity between the atoms).