Textbook 1D#23

[haley f]

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 know how to do part a, but I am confused on how the ml affects the number of orbitals, can someone please explain? Also for part c, how do we find the number of orbitals only knowing n?

[Andreas Krumbein 1L]

So for the n quantum number, you find that by looking at what subshell it's in (an electron in the 4s subshell has quantum number n=4, an electron in the 2p subshell has the quantum number n=2).
For the l quantum number, the number is found by looking at what orbital it's in (l=0 for the s orbital, l=1 for the p orbital, l=2 for the d orbital, l=3 for the f orbital).
For the ml quantum number, this represents the orientation of the angular momentum within the orbital, and can be found by looking at the order of this particular element on a periodic table, and the numbers that this can be range from l to -l.
The ms quantum number represents the electron's spin, and can be found by looking at the order of this particular element on a periodic table.

But to specifically answer your question, if you are given the subshell (n), and the subshell is 1, then there can only be 2 electrons with that quantum number, if the quantum number is 2, then only 8 electrons can have that quantum number, and if it's less than 4, then only 18 electrons can have that quantum number, and if its greater than 4, then only 32 electrons can have that quantum number. If you are given a subshell and an orbital (n and l) then there can only be 2, 6, 10, or 14 electrons in an atom that could have this quantum number (varies depending on the orbital in question), and if you are given the subshell, the orbital and the orientation, (n, l, and ml) then there can only be 2, 3, 5, or 7 electrons with this quantum number (also varies depending on the orbital, and s orbital is a sphere without orientation).

*I copied and pasted this from another question that I answered, but if you replace the word electrons with orbitals it should still be the same for your question.