# What are the four quantum numbers in chemistry?

Jun 7, 2018

$n$, $l$, ${m}_{l}$, and ${m}_{s}$.

#### Explanation:

Electrons can be described by $4$ quantum numbers. Here's a brief overview of each of them:

The first quantum number is called the principal quantum number, and it's denoted by the letter $n$. It represents the energy level/shell.

$n$ can equal any integer above and including $1$, since $n = 1$ represents the first principal energy level.

$n = 1 , 2 , 3 , 4. . .$

The second quantum number is called the orbital angular momentum number, and it's denoted by the letter $l$.
It represents the number of angular nodes (shown in the first image below) in an orbital, which means that it effectively represents the shape of the orbital.

The maximum value of $l$ is $n - 1$—the number of angular nodes in an orbital is always one less than the principal energy level.

$l = \text{0, 1, 2, 3, 4 ... (n-1)}$

The third quantum number is called the magnetic quantum number, and it's denoted by ${m}_{l}$. It describes the orientation of an orbital, which depends on the value of $l$.

${m}_{l} = - l , \ldots , 0 , \ldots , + l$

Our fourth quantum number is the electron spin number. It is denoted by ${m}_{s}$.

Essentially, every electron has a spin. This a spin is either in the direction of "up" or "down," denoted by the arrows $\uparrow$ and $\downarrow$ respectively.

$+ \frac{1}{2}$ represents $\uparrow$, and $- \frac{1}{2}$ represents $\downarrow$.

m_s = ±1/2