what does the sublevel designations s, p, d, and f specify with respect to the atomic orbitals

Question

what does the sublevel designations s, p, d, and f specify with respect to the atomic orbitals

Answer 1

Although Roman has answered the question quite thoroughly with respect to the accounting of electronic configurations one thing that was omitted is that the designations s, p, d, and f are referring to specific geometries for the  orbitals themselves. Those designated "s" are spherical, "p" are teardrop (my term) shaped with a node at the origin, "d" are teardrop and toroidal with a node at the origin,  and "f" are similarly teardrop and toroidal. Each increase in orbital complexity introduces more space for the electrons to occupy so that the "p" orbital have 2 lobes, "d" have 4 lobes, and "f" have 6-8 lobes; the exceptions being the  "d" and "f" toroidal orbitals.

In essence, they vary with respect to their orientation about the origin and the number of nodes (where there is zero probability of an electron to occupy that space). The more nodes, the higher the energy level that the electrons must have in order to occupy them.

Answer 2

In atoms, electrons orbit in shells corresponding to principal quantum number n. In increasing order of n, the shells are named K, L, M, N, O, P, ...

For a shell of principle quantum number n, there are subshells corresponding to orbital quantum numbers (lowercase L) l = 0, 1, 2, ... , n - 1. Their names are s,p,d,f,... in increasing order of l.

Furthermore, for each l, there are 2l+ 1 possible magnetic quantum numbers m_l = 0, ±1, ±2, ... , ±l.

Each state (n,l,m_l) can be occupied by up to 2 electrons maximum, which must have opposite spins (Pauli Exclusion Principle).

Also, there is a notation called spectral notation for electron configuration. I'm sure you have seen it.

It is a sequence of one ore more orbitals with their electron counts in the form

[shell number][subshell name]^{[number of electrons]}

Example, 1s²2s²2p⁶ for Neon means 2 electrons in subshell s of the n=1 shell, 2 electrons in subshell s of the n=2 shell, and 6 electrons in subshell p of the n=2 shell. The only subshell for n=1 and both subshells for n=2 are filled to capacity and no electrons occupy n>2 here, thus making Neon inert (Noble gas).