What are quantum numbers?

Question

6725 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-06-23T08:39:16

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

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

There are four quantum numbers for atoms:

$n = 1, 2, 3, . . .$ $n = 1, 2, 3, . . .$ - principal quantum number; describes the energy level.
$l = 0, 1, 2, . . ., n - 1$ $l = 0, 1, 2, . . . , n - 1$ - angular momentum quantum number; describes the shape of the orbital.
$0 \leftrightarrow s, 1 \leftrightarrow p, 2 \leftrightarrow d, 3 \leftrightarrow f, . . .$ $0 harr s, 1 harr p, 2 harr d, 3 harr f, . . .$ , etc. The ordering is $s, p, d, f, g, h, i, k, . . .$ $s,p,d,f,g,h,i,k, . . .$ .
$m_{l} = {- l, - l + 1, . . ., 0, . . ., l - 1, l}$ $m_l = {-l, -l+1, . . . , 0, . . . , l-1, l}$ - magnetic quantum number; corresponds to each unique orbital in the sublevel specified by $l$ $l$ , and there are $2 l + 1$ $2l+1$ such values.
$m_{s} = \pm \frac{1}{2}$ $m_s = pm1/2$ - spin quantum number; describes the spin (up/down)

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

chemwiki.ucdavis.edu