Give all possible ml values for orbitals that have each of the following: (a) l = 2; (b) n = 1; (c) n = 4, l = 3.

(a) ml = 0, ±1, ±2

(b) ml = 0

(c) ml = 0, ±1, ±2, ±3, ±4

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

So in our exercise,

(a) l = 2; equivalent with with sublevel d

-l ≤ ml ≤ l, ml = 0, ±1, ±2, equivalent with dxy, dxz, dyz, dx2-y2, dz2

(b) n = 1;

n = 1, only 01 level

l = 0, equivalent with sublevel s

ml = 0

(c) n = 4, l = 3.

l = 3, equivalent with sublevel f

ml = 0, ±1, ±2, ±3, ±4