Why can higher energy levels accommodate more electrons?
Because higher energy levels contain more orbitals.
As you know, the maximum number of electrons that a shell can hold is given by the formula
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
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
The third energy level has a total of
The fourth energy level has a total of
So, as a conclusion, higher energy levels can support more orbitals, which in turn means that they can hold more electrons.