Textbook question 1E.9

[Christine Nguyen 3D]

Of the following sets of four quantum numbers {n,l,ml,ms}, identify the ones that are forbidden for an electron in an atom and explain why they are invalid:
(a) {4,2,-1,+1/2} (b) {5,0,-1,+1/2} (c) 4,4,-1,+1/2}

How would one go about solving this?

Thanks!

[Claire_Latendresse_1E]

Hi! Option A is a perfectly valid set of quantum numbers.
Option B isn't valid because of the ml value. ml can only equal values from -l to +l. In this case, where l=0, ml can only be 0.
Option C isn't valid because of the l value. l can be any number from 0 to n-1. This l value violates that rule because l=n (illegal!!!!). There's no 4g orbital.

[Natalie Do 3F]

To elaborate, a is valid because
2 is less than 4
-1 is between -2 and 2
-1/2 is one of your options for ml

[Earl Garrovillo 2L]

It'd first be helpful to remember the "bounds" of the quantum number and that the numbers are ordered by {n, l, ml, ms}. l can be 0 to (n-1), ml can be -l to +l (including 0), and ms can only be +1/2 or -1/2.
Given these bounds, we can say that (a) is valid set of quantum numbers since none of the bounds are violated,
(b) is not a valid set because even though l=0 is valid, since l=0, ml can only be between -0 an +0 (basically ml has to be 0 when l=0)
(c) is not valid because the maximum value of l is n-1. Since n is 4, the maximum value of l is 3 but here, l=4 so this set is invalid.

[ShinwooKim_3E]

The main exceptions I look for is that s never equals 0 and l cannot be more than 4!