# How many electrons have #n = 3#, #m_l = 0#, and #m_s = +1/2#?

##### 1 Answer

#### Answer:

Three electrons.

#### Explanation:

The idea here is that each electron in an atom has an **unique set** of quantum numbers, which describes exclusively that electron.

The four quantum numbers are

In your case, the only quantum number that is not accounted for is the *angular momentum quantum number*, *principal quantum number*.

So, the question wants you to find the number of electrons that

can be located on the third energy level, since#n=3# ;can be located in an orbital that has a specific orientation, since#m_l=0# have spin-up, since#m_s = +1/2#

Start by finding how many **orbitals** can accomodate these electrons. SInce you know what the relationship of

#l = 0, 1, ..., (n-1) implies l = {0; 1; 2}#

For **s-orbital**, you can have one electron located in the **3s-orbital** that has spin-up.

For **3p-orbitals**, you can have an electron located in the

Finally, for **3d-orbitals**, you can have an electron located in the

Therefore, these quantum numbers can correspond to a total of **three electrons**

#n=3" " l=0" "m_; = 0" "m_s = +1/2# #n=3" "l=1" "m_l = 0" "m_s = +1/2# #n=3" "l=2" "m_l = 0" "m_s = +1/2#