Final answer:
The number of orbitals for n=7, l=3, m=-1 is one, as the magnetic quantum number m=-1 specifies one of the seven f orbitals in the f subshell.
Step-by-step explanation:
The question asks how many orbitals are in the set defined by quantum numbers n=7, l=3, m=-1. The quantum number l indicates the subshell type, where l=0 is an s subshell, l=1 is a p subshell, l=2 is a d subshell, and l=3 corresponds to an f subshell.
For the f subshell (l=3), there are a total of seven possible orientation values for the magnetic quantum number ml, ranging from -3 to +3. This means there are seven unique f orbitals, each with a specific three-dimensional orientation. Since the number of orbitals is determined by the value of l, and not by the particular value of ml, the answer to the question is one orbital for ml=-1 within the f subshell.