What limits the number of orbitals in each quantum level?
In our study of one-dimensional quantum mechanics you learned that there is just one way to have any particular number of nodes and that orbital energies increase monotonically with the number of nodes. Nodes mark the division between adjacent regions of positive and negative wave function. In one dimension nodes are points; in two dimensions they are lines; in three dimensions, surfaces. The point of giving you this table is not to make you suffer with algebra, and certainly not to make you memorize all the formulae. The idea is to help you have the fun of constructing a few real wave functions and using them to ask such questions as “Where is the highest density in the electron cloud of a 2p or a 2s orbital?” and “What does an orbital really look like; have books and teachers been telling me the truth or not?” Exact electronic wave functions can be written down only for this kind of one-electron atom. As soon as a second electron is included, you have to worry about two more potentia