Chem – Quantum Numbers (Part 3)

What sections should I know before attempting to learn this section?

—> Orbitals Part 1

—> Energy Level Part 2

—> Complete Electron Configuration Part 3

—> Quantum Numbers Part 1 (n)

—> Quantum Numbers Part 2 (L)


What does the mL stand for in the quantum numbers?

The next quantum number category mL (it is pronounced “M sub L”) stands for the specific orbital within the orbital types. This relates back to how many orbitals each orbital type has. The s orbitals have one orbital each. The p orbitals have 3 orbitals each. The d orbitals have 5 orbitals each. The f orbitals have 7 orbitals each. The mL depends on the (L). The table below will show you best how ml is dependent on (L).

If (L) is Then mL can be… Orbital types # of electrons # of orbitals
L = 0 0 s 2 1
L = 1 -1, 0, 1 p 6 3
L = 2 -2, -1, 0, 1, 2 d 10 5
L = 3 -3, -2, -1, 0, 1, 2, 3 f 14 7

Notice in the table above the two columns I highlight in red are related. On the bottom row there are 7 integers running from negative 3 to positive 3. Each one of those integers represents an individual orbital among that orbital type. Again you can reference the quantum periodic table to show you better where they are and how they are arranged. Keep in mind that different teachers like to display them in slightly different ways. The way I demonstrate on the periodic table seems to be the easiest to understand but it is not the only way to understand this concept.


Examples: Give the mL for the last electron in the following elements.

Be mL = 0
Pd mL = 1
Al mL =-1


PRACTICE PROBLEMS: Give the mL for the last electron in the following elements.

K mL = 0
S mL = 0
Ge mL = -1
Ti mL = -2
Au mL = 2
Lu mL = 3


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