# Question #f0e05

##### 1 Answer

Here's my take on this.

#### Explanation:

I assume that you're interested in finding out *how many electrons* can share those two quantum numbers

#n=4" "# and#" "m_s = -1/2#

The idea here is that you can use the fact that the **number of orbitals** each *energy level* can hold is given by the equation

#color(blue)(|bar(ul(color(white)(a/a)"no. of orbitals" = n^2color(white)(a/a)|)))#

Here

*principal quantum number*, the quantum number that gives you the **energy level** on which the electron resides

In your case, the *fourth energy level* will have a total of

#"no. of orbitals" = 4^2 = 16#

This tells you that the fourth energy level can hold a total of **orbitals**. Since each orbital can hold a *maximum* of **electrons**, it follows that the maximum number of electrons that can share the quantum number

#"no. of e"^(-) = 2 xx "16 orbitals" = "32 e"^(-)#

Now, **half** of these electrons will have *spin-up*, which is given by *spin-down*, which is given by

Since you're interested in the number of electrons that have

#"no. of electrons" = "32 e"^(-)/2 = color(green)(|bar(ul(color(white)(a/a)color(black)("16 e"^(-))color(white)(a/a)|)))#