yes these orbitals can exist. Rules are algorithms, by which we generate possible quantum numbers. The lowest value of n
is 1 (NOT zero). For n
= 1, the only possible value for quantum number l
is 0, and m
= 0. Each set of quantum numbers is called a state
. Thus, for n
= 1, there is only one state (1,0,0). The states are represented by symbols, and special symbols have been used to represent the quantum number l
l = 0, 1, 2, 3, 4, ...
symbol = s, p, d, f, g, ...
The three quantum numbers (q.n.) n, l, m follow the rules:
for the principal q.n. n
azimuthal q.n. l = 0, 1, 2, ..., n-1
magnetic q.n. m = -l, -(l-1), ..., (l-1), l
So, these orbitals are possible.