Textbook Problem 1D.23 Orbitals

[Vanessa_Ong_3F]

I think I have the wrong understanding of this question, can somebody help reexplain this question to me please? I do not understand how we got 1 for part b. I thought that since l=2 and it is in the d-orbital, there would be 5 orbitals?

How many orbitals can have the following quantum numbers in an atom: (a) n=2, l=1; (b) n=4, l=2, ml=-2; (c) n=2; (d) n=3, l=2, ml=+1?

[Tyler_Kim_2G]

The possible magnetic quantum numbers when l=2 are -2, -1, 0, 1, and 2, which is probably why you thought the answer was five. I think the answer here is one orbital, however, because the problem specifically stated that the magnetic quantum number was -2.