# What are some examples of quantum numbers?

Jul 10, 2018

There are four quantum numbers...,

#### Explanation:

and they are $n , l , {m}_{l} , {m}_{s}$. Each specifies a different meaning and its function.

$n$ is the principal quantum number and states the energy level of an electron. You can think of it as the electron shell number. It can only be a whole number greater than 0, i.e. $n > 0 , \forall n \in \mathbb{Z}$.

$l$ is the angular momentum number and specifies the subshell $\left(s , p , d , f , \ldots\right)$ of an atom. It therefore determines the shape of the orbital. The conditions are such that $l = 0 , 1 , 2 , 3 , 4 , \ldots , \left(n - 1\right)$.

${m}_{l}$ is the magnetic angular momentum number, and determines the number of orbitals in the subshell. The conditions are such that ${m}_{l} = - l , \left(- l + 1\right) , \left(- l + 2\right) , \ldots , - 2 , - 1 , 0 , 1 , 2 , \ldots , \left(l - 2\right) , \left(l - 1\right) , l$.

${m}_{s}$ is the electron spin number and states the direction spin of an electron. It only has two values and does not depend on another quantum number. Conditions are that ${m}_{s} = \pm \frac{1}{2}$. Positive $\frac{1}{2}$ means an $\uparrow$ spin while negative $\frac{1}{2}$ designates a $\downarrow$ spin.