Question

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

Answer 1

`32`

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 `n` is the 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 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.

`"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 `16` orbitals and a maximum of `32` electrons.