Which set(s) of three quantum numbers is(are) permissible?
I. n = 2, = 1, and = 1
II. n = 4, = 2, and = - 2
III. n = 3, = 3, and = 0

Question

Which set(s) of three quantum numbers is(are) permissible?
I. n = 2,  = 1, and  = 1
II. n = 4,  = 2, and  = - 2
III. n = 3,  = 3, and  = 0

Quizplus · Accepted Answer

For a given electron, the three quantum numbers n, l, and ml must satisfy the following conditions:
1. n must be a positive integer (n = 1, 2, 3...)
2. l must be an integer between 0 and n-1 (l = 0, 1, 2, ..., n-1)
3. ml must be an integer between -l and +l (ml = -l, -l+1, ..., 0, ..., l-1, +l)
Using these rules, we can check each set of quantum numbers:
I. n = 2, l = 1, and ml = 1 or -1
These values of n, l, and ml are permissible, so set I is allowed.
II. n = 4, l = 2, and ml = +2 or -2
These values of n, l, and ml are permissible, so set II is allowed.
III. n = 3, l = 3, and ml = 0 or ±1 or ±2 or ±3
The value of l cannot be greater than n-1, so set III is not allowed.
Therefore, the only sets of quantum numbers that are permissible are I and II, so the answer is D.

Which Set(s) of Three Quantum Numbers Is(are) Permissible