Every atom has an infinite number of atomic orbitals. Orbitals differ in size, shape, and direction (orientation) — and each of those facets is tied to a quantum number. This module teaches you how orbitals are organized in terms of quantum numbers, and how that organization relates to shells, subshells, and individual orbitals.
Electron orbitals are grouped into shells, numbered from 1 upward. This number, n, is the principal quantum number, and the larger it is, the larger the orbital.
Each shell has one or more subshells. Each subshell contains orbitals of similar shape. The subshell types used by real atoms are s, p, d, and f. Each shape is associated with the angular momentum quantum number, l. The possible l values for an orbital can range from zero to one less than the n value.
| Subshell | Shape | l |
|---|---|---|
| s | spherical | 0 |
| p | dumbbell | 1 |
| d | cloverleaf | 2 |
| f | three-dimensional | 3 |
Quantum numbers for subshells are therefore:
| Shell | Subshells |
|---|
Multiple orbitals can exist within a single subshell. These are designated by the direction of their lobes, like px, py, and pz, and are associated with the magnetic quantum number, ml. The possible ml values range from −l to +l. The possible values for orbitals in s, p, d, and f subshells are:
| Subshell | l | ml values |
|---|---|---|
| s | 0 | 0 |
| p | 1 | −1, 0, +1 |
| d | 2 | −2, −1, 0, +1, +2 |
| f | 3 | −3, −2, −1, 0, +1, +2, +3 |
The different ml values are not tied to specific direction designations. A p subshell has three orbitals, px, py, and pz, and those orbitals have ml values of −1, 0, and +1 — but the px orbital isn't defined by any one specific ml value among the three.
Now it's time to practice. There are four levels: finding n, finding l, finding the possible ml values, and deciding whether a full set of quantum numbers describes an orbital that actually exists. Each level has a reference sheet you can pop open at any time.