Question

Are the following quantum number combinations allowed? If not, show two ways to correct them:

Answer 1

Answer:

(a) n = 2; l = 0; ml = -1 ⇒ WRONG

change ml = 0, or l = 1 to correct.

(b) n = 4, l = 3; ml = -1 ⇒ CORRECT

(c) n = 3, l = 1; ml = 0 ⇒ CORRECT

(d) n = 5, l = 2; ml = +3 ⇒ WRONG

change ml = 0, ±1 or ±2, or l = 3 or l = 4 to correct.

Explanation:

The rules for electron quantum numbers are:

1. Shell number, 1 ≤ n

2. Subshell number, 0 ≤ l ≤ n − 1

3. Orbital energy shift, -l ≤ ml ≤ l

4. Spin, either -1/2 or +1/2

Now, apply in our case

(a) n = 2; l = 0; ml = -1 ⇒ WRONG

-l ≤ ml ≤ l, so either change ml = 0 or l = 1 to correct.

(b) n = 4, l = 3; ml = -1 ⇒ CORRECT

(c) n = 3, l = 1; ml = 0 ⇒ CORRECT

(d) n = 5, l = 2; ml = +3 ⇒ WRONG

-l ≤ ml ≤ l, so either change ml = 0, ±1 or ±2, or l = 3 or l = 4 to correct.