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

Feb 8, 2018

$32$

#### Explanation:

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

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{\text{no. of e}}^{-} = 2 {n}^{2}}}}$

Here $n$ is the principal quantum number that describes the energy shell.

$n = 4$

which means that

${\text{no. of e}}^{-} = 2 \cdot {4}^{2} = 2 \cdot 16 = 32$

This means that the fourth energy shell can hold a maximum of $32$ electrons.

As you know, each orbital can hold a maximum of $2$ 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.

$\text{no. of orbitals} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} {n}^{2}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} = {n}^{2}$

In your case, the fourth energy shell can hold $16$ orbitals and a maximum of $32$ electrons.