# What are four quantum numbers for a K atom?

Apr 15, 2016

$4 , 0 , 0 , \pm \frac{1}{2}$

#### Explanation:

The four quantum numbers for an atom refer to the state of the valence or outermost electron.

The four numbers are:

$n$ is the distance of the electron from the nucleus, and can be $1 , 2 , 3 , 4$ etc,
$l$ is the shape of the orbital of the electron, from $0$ to $n - 1$
${m}_{l}$ is the orientation of the orbital, ranging from $- l$ to $+ l$, and
${m}_{s}$ is the spin property of the electron, either $+ \frac{1}{2}$ or $- \frac{1}{2}$

For a potassium atom, the electron configuration is $1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {s}^{2} 3 {p}^{6} 4 {s}^{1}$, which means that $n = 4$.

It also means that, since the outermost electron is in an $s$ orbital, $l = 0$.

${m}_{l}$ can range from $- l$ to $+ l$, but if $l = 0$ because it is an $s$ orbital, then ${m}_{l}$ must be $0$, too.

${m}_{s}$ can be either $+ \frac{1}{2}$ or $- \frac{1}{2}$, depending on the spin of the electron, it doesn't particularly matter in this case.

Therefore, the full set of quantum numbers for a $K$ atom is $4 , 0 , 0 , \pm \frac{1}{2}$