# How many sets of quantum numbers are possible when n=3?

Dec 4, 2015

$18$

#### Explanation:

As you know, each electron that's part of an atom has its own unique set of four quantum numbers that describes its position and spin.

This means that looking for the number of unique sets of quantum numbers is equivalent to looking for the number of electrons that can occupy the third energy level.

As you know, the number of orbitals you get per energy level is given by the equation

color(blue)("no. of orbitals" = n^2)" ", where

$n$ - the principal quantum number, the ones that gives the energy level.

So, if you're dealing with the third energy level, you can say that it will contain a total of

$\text{no. of orbitals} = {3}^{2} = 9$

distinct orbitals.

Now, each orbital can contain a maximum of $2$ electrons of opposite spins. This means that the third energy level will contain a maximum number of

${\text{no. of electron" = 9 * 2 = "18 e}}^{-}$

So, if each electron is described by an unique set of quantum numbers, you can conclude that $18$ sets of quantum numbers are possible for the third energy level.