1D. 23

[JamieVu_2C]

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?

For (b) and (c), how does the magnetic quantum number tell you how many orbitals there are? I don't understand how to find the number of orbitals with ml.

[Chem_Mod]

Ml denotes more specifically the particular orbital that the electron occupies. For example, for l=1 and ml= -1, this would denote the px, py, or pz orbital (but only one of these three), whereas just l=1 would only tell you that the electron is in the p orbital

[JamieVu_2C]

So for c, would that mean there is only one orbital for the given quantum numbers?

[Kayli Choy 2F]

For c, if n=2, that means that the possible orbitals are
n = 1, l = 0
and
n = 2, l = 1
n = 2, l = 0
n = 2, l = 1
because the allowed values of l are -(n-1) to (n-1).
Therefore, there are four possible orbitals for n=2.

[105311039]

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?

For (b) and (c), how does the magnetic quantum number tell you how many orbitals there are? I don't understand how to find the number of orbitals with ml.

-Ml specifically denotes which orbital we should be looking for in the question, so for b) we know that Ml has values from (-l,l) so its telling us that this quantum number only has 1 orbital because it is looking at that one specific orbital.
- For C) you are looking at when n=2, so you know when n=2 there can be possible 8 electrons total, and you know that each orbital can hold 2 electrons. So therefore, for 8 total electrons there will be 4 orbitals.