# How would you find the quantum numbers for an atom?

Dec 1, 2015

See explanation.

#### Explanation:

Quantum numbers are considered as the coordinates that will give an idea about the location of an electron in an atom.

There are four different quantum numbers:

1. Principal Quantum Number (n) has integral values 1, 2, 3, ... This number determines the size and energy of the orbital.
2. Angular Momentum Quantum Number ($l$) associated with the number of different types of subshells in an energy level. $l = 0 , 1 , 2 , 3 , \ldots \left(n - 1\right)$. 3. Magnetic Quantum Number (${m}_{l}$) describes the orientation (direction) in space of each orbital and can have integral values from $- l$ through $+ l$. 4. Electron Spin Quantum Number (${m}_{s}$) describes the direction of spin of the electron(s) in an orbital. There are only two values of ${m}_{s} , + \frac{1}{2} \text{and} - \frac{1}{2}$.

Note that no two electrons may have identical sets of all 4 quantum numbers.

Consider the electron configuration of sodium ""_11Na:

""_11Na:1s^(2)2s^(2)2p^(6)color(red)(3)color(blue)(s)^(color(green)(1))

What would be the set of quantum numbers of the valence electron of sodium:
$\textcolor{red}{n = 3}$: third energy level.
$\textcolor{b l u e}{l = 0}$: sublevel or subshell $s$.
$\textcolor{b l u e}{{m}_{l} = 0}$: one possible orbital.
$\textcolor{g r e e n}{{m}_{s} = + \frac{1}{2}} \mathmr{and} \textcolor{g r e e n}{- \frac{1}{2}}$: the electron spin.