CHEMISTRY COMMUNITY

For the P-orbital, we use the subscripts x,y, and z. In class, he said something about how these only work if we explicitly define each level as x, y, and z. Does this mean we can use other symbols instead of these to define the different sets of electrons?

Yes, you could in theory. However, x, y, and z are the standard labeling conventions for the different p orbitals.

Like the answer above said, I'm pretty sure changing them up would be okay. At the same time however, I think we are trying to imply viewing things in three dimensions in which case the most logical variables to use are x, y, and z as you would for a 3 dimensional set of coordinates.

Just a reiteration, but yes you could switch those variables. They serve the purpose of showing the orbital is three dimensional.

Would we have to know the sub orbitals for d and f?

In response to your questions about d and f, I don't think we would have to know the exact ones since there are so many and since they are also harder to draw than the p orbital