# How many electrons can fill the energy shell described by the principal quantum number #n=4# ?

##### 1 Answer

#### Explanation:

All you need to remember here is that the number of electrons that can occupy a given energy shell is given by

#color(blue)(ul(color(black)("no. of e"^(-) = 2n^2)))#

Here *principal quantum number* that describes the energy shell.

In your case, you have

#n =4#

which means that

#"no. of e"^(-) = 2 * 4^2 = 2 * 16 = 32# This means that the

fourth energy shellcan hold a maximum of#32 # electrons.

As you know, each **orbital** can hold a maximum of **electrons**, as stated by **Pauli's Exclusion Principle**. This means that you can use this equation to find the total number of orbitals that are present in a given energy level.

#"no. of orbitals" = (color(red)(cancel(color(black)(2)))n^2)/color(red)(cancel(color(black)(2))) = n^2#

In your case, the fourth energy shell can hold **orbitals** and a maximum of **electrons**.