# How would you find out the number of electrons from just the 4 quantum numbers?

##### 1 Answer

Here's what I would suggest.

#### Explanation:

If a **complete set** of quantum numbers is given to you, then you can say for a fact that you're only dealing with **one electron**.

As you know, quantum numbers are used to describe the location and spin of an electron that surrounds an atom's nucleus.

More specifically, the *four* quantum numbers will tell you

*the energy level on which the electron resides*- given by#n# , the**principal quantum number***the subshell in which the electron resides*- given by#l# , the**angular momentum quantum number***the exact orbital in which you can find the electron*- given by,#m_l# , the**magnetic quantum number***the spin of the electron*- given by#m_s# , the**spin quantum number**

Now, each *complete set* of quantum numbers can **only describe one electron**. This means that if you're given something like this

#n=2, l=1, m_l = 0, m_s = +1/2#

then you know for a fact that only one electron can have that set of quantum numbers.

Now, let's assume that you are not given all four quantum numbers. These are some rules to help you figure out how many electrons can share an *incomplete* set of quantum numbers

*You are given the value of*#n#

If this is the case, then use the fact that the number of *electrons* you get per energy level is equal to

#color(blue)("no. of electrons" = 2n^2)#

*You are given*#n# *and*#l#

This time, you know the energy level **and** the subshell in which the electrons can be found. To determine how many electrons can share these quantum numbers, use

Once you know how many *orbitals* you have **per subshell**, multiply that value by

#color(blue)("no. of electrons" = 2 xx "no. of subshells")#

*You are ginve*#n# ,#l# ,*and*#m_l#

Now you know the energy level, subshell, **and** specific orbital in which the electrons can reside.

Since the only possible values for **every orbital** can hold a **maximum** of two electrons.