Textbook Problem 1D.23

[cadytran1K]

How many orbitals can have the following quantum numbers in an atom: (b) n=4, l=2, = -2

Hi! I'm studying for the midterm and I'm confused as to why when:
n = 4,
l = 2,
= -2

The number of orbitals is 1. Shouldn't it be 5 orbitals because the atom is at the 4d state?

[Courtney Situ 2B]

Hi!

It's true that the 4d subshell has 5 orbitals (-2, -1, 0, +1, +2). However, this information only fits with n = 4 and l = 2. The question adds on that the magnetic quantum number must be -2. This refers to only one of the 5 orbitals (the one marked -2), so the answer is one orbital (only one orbital fits n = 4 and l = 2, and ml = -2).

Hope this helps!

[Q Scarborough 1b]

You are correct that the 4d state has 5 orbitals, but this problem specifies the ml number as -2, which corresponds to only one orbital.

[cadytran1K]

Hi!

It's true that the 4d subshell has 5 orbitals (-2, -1, 0, +1, +2). However, this information only fits with n = 4 and l = 2. The question adds on that the magnetic quantum number must be -2. This refers to only one of the 5 orbitals (the one marked -2), so the answer is one orbital (only one orbital fits n = 4 and l = 2, and ml = -2).

Hope this helps!

Ohh this makes a lot more sense, thank you!