How Many Electrons Can Each Energy Level Hold (2n²)?

For IB Chemistry SL and HL, the maximum number of electrons in a main energy level is calculated using $2n^2$, where $n$ is the principal quantum number. The first four energy levels can therefore hold a maximum of 2, 8, 18, and 32 electrons respectively.

How the Rule Works

A main energy level, also called an electron shell, is identified by $n=1, 2, 3,$ and so on. Each main energy level contains $n^2$ orbitals, and each orbital can hold a maximum of two electrons with opposite spins.

Therefore:

$$\text{maximum number of electrons}=2\times n^2$$

For example, for the third energy level:

$$2n^2=2(3)^2=2(9)=18\text{ electrons}$$

The capacities can also be understood from the sublevels present. The first level contains only the $1s$ sublevel, while the second contains $2s$ and $2p$. An $s$ sublevel holds 2 electrons, a $p$ sublevel holds 6, a $d$ sublevel holds 10, and an sublevel holds 14.

This gives another way to verify the rule. In the third level, the $3s$, $3p$, and $3d$ sublevels contain 1, 3, and 5 orbitals respectively. That is 9 orbitals in total, so the capacity is $9\times2=18$ electrons. Similarly, the fourth level has 16 orbitals and therefore a capacity of 32 electrons. This relationship describes capacity, not the order in which sublevels fill.

A common misconception is that each energy level must become completely full before electrons enter the next level. This is incorrect because electrons occupy orbitals in order of increasing energy, not simply increasing $n$. For example, the $4s$ orbital is occupied before the $3d$ orbitals in neutral atoms.

Exam Technique

This is assessed in Structure 1.3: Electron configurations. For a “calculate” question, substitute the given value of $n$ into $2n^2$ and show the working. Do not confuse the maximum shell capacity with the actual number of electrons present in an atom’s ground-state electron configuration.