I was wondering, does the principal quantum number refer to the electron shell.
Okay, I think I figured it out. The way my chemistry textbook explains gives the impression that the principal number corresponds to the electron shell; but it really signifies the overall size and energy of an orbital in a particular electron shell. Since it is a chemistry textbook, I am assuming they are only talking of principal numbers in terms of the 1st shell electron shell. Is that correct?
The principle quantum number, n, tells you the energy. The other two quantum numbers l and m tells you about the orbital angular momentum. To denote which shell exactly, you need all three (n,l,m), but if you just wanted to know the energy (to first approximation), you only need n.
If you wanted the exact energy, you still need to take l and m (and the spins of the proton and electron), depending on your requirement for accuracy.
Separate names with a comma.