For each of the following, give the sublevel designation, the allowable ml values, and the number of orbitals:

(a) n = 2, l = 0

(b) n = 3, l = 2

(c) n = 5, l = 1

(a) n = 2, l = 0 ⇒ sublevel s, ⇒ ml = 0, number of orbitals = 1

(b) n = 3, l = 2 ⇒ sublevel d, ⇒ ml = 0, ±1, ±2, number of orbitals = 5

(c) n = 5, l = 1 ⇒ sublevel p, ⇒ ml = 0, ±1, number of orbitals = 3

Explanation:

The rules for electron quantum numbers are:

1. Shell number, 1 ≤ n,

2. Subshell number, 0 ≤ l ≤ n - 1, from s, p, d, f, g, h ...

3. Orbital energy shift, - l ≤ ml ≤ l

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

In our case

(a) n = 2, l = 0 ⇒ sublevel s

-l ≤ ml ≤ l ⇒ ml = 0, number of orbitals = 1

(b) n = 3, l = 2 ⇒ sublevel d

-l ≤ ml ≤ l ⇒ ml = 0, ±1, ±2, number of orbitals = 5

(c) n = 5, l = 1 ⇒ sublevel p

-l ≤ ml ≤ l ⇒ ml = 0, ±1, number of orbitals = 3