Homework 1D. 23

[ayushibanerjee06]

Can someone explain 1D. 23 for me?
The question is 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?
I don't understand how to do this question, I know what the quantum numbers are but don't know where to go from there.

[ayushibanerjee06]

I understand why a) is 3 orbitals, but I don't understand why b) is 1 orbital and not 5 since it's 4p, why c) is 4 orbital and not 1, and why d) is 1 orbital and not 7

[AniP_2D]

(a) a is 3 orbitals because the possible outcomes for ml are -1, 0, 1
(b) b is only 1 orbital because the value of ml is already given to you. Since only 1 value of ml is given (ml=-2), there is only 1 orbital
(c) for n=2, the possible l values are 0 and 1. The possible ml values for l=0 are ml=0 and for l=1, ml=-1, 0, 1. When you coming these you get 4 values which is why there are 4 orbitals
(d) Once again, since they give you the value of ml (ml=+1), you only have 1 orbital .