# How many electrons can be added to the fifth energy level?

Dec 7, 2016

${\text{50 e}}^{-}$

#### Explanation:

The maximum number of electrons that can occupy a given energy level $n$ is given by

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

The idea here is that the number of orbitals that are present in an energy level $n$ is given by

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

As you know, a given orbital can hold a maximum of $2$ electrons, which is why the maximum number of electrons that can be added to a given energy level $n$ is twice the number of orbitals present on said energy level.

In your case, $n = 5$, which refers to the fifth energy level, holds

$\text{no. of orbitals} = {5}^{2}$

$\text{no. of orbitals} = 25$

This means that the maximum number of electrons that can be added to the fifth energy level is

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{max no. of e"^(-) = 2 * 25 = "50 e}}^{-}}}}$