Question

Given a set of quantum numbers, determine whether each is permitted for an orbital in an atom.

(a) n = −2, l = 0, ml = 0
(b) n = 3, l = 1, ml = 0
(c) n = 2, l = 1, ml = −1
(d) n = 3, l = 0, ml = 5
(e) n = 4, l = 4, ml = 3

Answer 1

In quantum mechanics, there are certain restrictions on the values of quantum numbers for orbitals in an atom. Sets of quantum numbers that follow these restrictions are allowed, while sets that violate the restrictions are not allowed.

Step-by-step explanation:

a. The principal quantum number n must be an integer, as it is here. The quantum number l must be less than n, which it is. The magnetic quantum number ml must be between -l and l, which it is. The spin quantum number ms is +1/2, which is allowed. Because this set of quantum numbers follows all restrictions, it is possible.

b. The quantum number n is an integer, but the quantum number l must be less than n, which it is not. Thus, this is not an allowed set of quantum numbers.

c. The principal quantum number n is an integer, but l is not allowed to be negative. Therefore, this is not an allowed set of quantum numbers.