# Why can higher energy levels accommodate more electrons?

Jun 10, 2015

Because higher energy levels contain more orbitals.

#### Explanation:

As you know, the maximum number of electrons that a shell can hold is given by the formula

$\text{no. electrons} = 2 {n}^{2}$, where

$n$ - the energy level.

Electrons that surround a nucleus can be found in orbitals, with each orbital having a maximum capacity of 2 electrons. You can determine the number of orbitals an energy level has by using this formula

$\text{no. orbitals} = \frac{2 {n}^{2}}{2} = {n}^{2}$

This tells you that higher energy levels have more orbitals available for electrons to occupy. The first energy level only has 1 orbital, so its capacity is limited to 2 electrons.

The second energy level has a total of ${2}^{2} = 4$ orbitals ,so it can hold up to 8 electrons.

The third energy level has a total of ${3}^{2} = 9$ orbitals, so its capacity is 18 electrons.

The fourth energy level has a total of ${4}^{2} = 16$ orbitals, so its capacity is 32 electrons.

So, as a conclusion, higher energy levels can support more orbitals, which in turn means that they can hold more electrons.