Textbook 1D #23

[Anh Trinh 1J]

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

Whenever we are given the quantum ml number, is it always only going be 1 orbital? I understand why (b) is 1 orbital, but I'm not sure for (d). Since ml=+1, I thought it would be 4 orbitals, but the answer is 1 orbital.

[Rich Luong 1D]

Essentially it really depends. In this case, yes, since they've given you one single ml value, there will only be one orbital. Pretend these numbers to be like coordinates for you, the more specific it becomes, the less orbitals there are. In (b), it's one orbital because the numbers are being very specific and telling you that the orbital is located in a 4d location but only pinpointing ONE single orbital, which is ml= -2. Same case for (d). The orbital is located in the 3d location but is only pinpointing ONE single orbital, which is ml = +1. So essentially, the location and amount of ml values given to you is how many orbitals there are. If there are 2 ml values, there are two orbitals and so on. I hope this helps!

[Sahaj Patel Lec3DisK]

Since the ml position is exactly one number, then that series of numbers can only be representative of one elements. If there were more ml numbers, then there would possibly be more elements with that pair of quantum numbers. Hope this helps!

[Daria Obukhova 2B]

In this question when it says ml, it will be one orbital. For example, if n=2 and l=1, there'd be three possible orbitals px,py,pz. Then, the ml number specifies which one it is.
Also for part d, there would technically be 5 possible orbitals, but they specified it with the ml number.

[RitaThomas_3G]

Although theoretically there could be more possible orbitals, because the question specified exactly which ml value it is (+1), there is only 1 possible orbital.