Joanne Lee
- Feb 27, 2021
- 3 min read

Quantum Numbers

By: Khushi Gupta

Just reading this title, quantum numbers must sound like a hard topic to understand from the use of the word “quantum.” We see this word around a lot in pop culture, especially Marvel movies like Ant-man where they delve into the quantum realm for various adventures. Quantum numbers, however, branch from the chemistry side of science as it is a set of numbers that describe an electron in an atom.

There are four numbers used to completely describe the electron: principal quantum number (n), angular momentum (l), magnetic quantum number (ml), spin quantum number (ms).

The principal quantum number describes the energy level and orbital size. It can be any number from 1 and higher. To find this, one must simply look at the row number on the periodic table.

The angular momentum number describes the shape of the orbital and divides the orbitals into smaller groups called subshells or sublevels. There are different letters used to correspond to each subshell to avoid confusion but numbers are used when writing in proper format. The l value ranges from n-1 as the first subshell s is l = 0, the second subshell p is l= 1 and so on.

The magnetic quantum number describes the orientation of the shell and divides the subshells into singular orbitals that hold electrons. Each subshell has 2l +1 orbitals. This means that the s subshell would have only 1 orbital, the p subshell would have 3 and so on. The value of ml ranges from -l to l. As the s subshell only has 1 orbital, the value of ml of the electron will always be 0. The p subshell has 3 so the electron’s ml value would be either -1,0, or 1.

The spin quantum number is the orientation of the spin axis of an electron and can either be +½ (spin up) or -½ (spin down). This is the easiest to remember out of the 4 numbers as there are only 2 possible values. Looking at electron energy diagrams, an arrow pointing upwards corresponds to the ½ while the down arrow represents the -½ .

Putting all the numbers together, you would have a list of numbers that correspond to (n, l, ml, ms).

When starting out with quantum numbers, the easiest way to learn how to use them is by referencing the periodic table. The principal quantum number (n) is just the period or row number of the element. So if we were finding the quantum number of the last electron in a neutral Silicon (Si) atom, n would equal 3. For the angular momentum number (l), it can be seen that the element Si is located in the p block section meaning that l = 1. The sections are divided in the periodic table so that when looking for electrons in neutral atoms the first two columns/groups are the s subshells, the last 6 are the p subshells, and the ones in between are the d subshells. The two columns underneath (Lanthanides and Actinides) are f subshells. Since we know that the p subshell has 3 orbitals it can be either -1, 0 or 1. To find this, we look at the six columns within the periodic table that correspond to the p subshell. The pattern is that the first and fourth column is -1, the second and fifth is 0, and the third and sixth is 1. Silicon is located in the second column so m = 0. The spin quantum number is +½ as Silicon lands in the first three columns in the p block. If it was located in the last three columns (like the element Chlorine), it would have a negative spin. In all, the quantum numbers for the electron would be (3, 1, 0, ½).