What are quantum numbers?

Jun 23, 2014

Quantum numbers can be used to describe the quantum state of an electron.

Explanation:

Quantum numbers can be used to describe the quantum state of an electron.

There are four quantum numbers for atoms:

1. $n = 1 , 2 , 3 , . . .$ - principal quantum number; describes the energy level.

2. $l = 0 , 1 , 2 , . . . , n - 1$ - angular momentum quantum number; describes the shape of the orbital.
$0 \leftrightarrow s , 1 \leftrightarrow p , 2 \leftrightarrow d , 3 \leftrightarrow f , . . .$, etc. The ordering is $s , p , d , f , g , h , i , k , . . .$.

3. ${m}_{l} = \left\{- l , - l + 1 , . . . , 0 , . . . , l - 1 , l\right\}$ - magnetic quantum number; corresponds to each unique orbital in the sublevel specified by $l$, and there are $2 l + 1$ such values.

4. ${m}_{s} = \pm \frac{1}{2}$ - spin quantum number; describes the spin (up/down)

A given orbital is labeled as an $n l$ orbital: