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

##### 1 Answer

#### 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

*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

#"no. of orbitals" = 3^2 = 9#

distinct orbitals.

Now, each orbital can contain a *maximum* of

#"no. of electron" = 9 * 2 = "18 e"^(-)#

So, if each electron is described by an unique set of quantum numbers, you can conclude that