Atomic Shells

Shells as Energy Levels

In the simple Bohr model, electrons are shown in atomic shells, which represent specific energy levels around the nucleus. A shell closer to the nucleus has lower energy. A shell farther from the nucleus has higher energy.

OpenStax explains that the Bohr model uses orbits with specific energies to explain the line spectrum of hydrogen. The reference is available at openstax.org.

Picture a building with floors. The first floor is near the ground, the second floor is higher, and so on. In an atom, the "floor" is not a physical floor. It is an energy level. So, a circular shell diagram is an energy-level sketch, not a rigid track that electrons follow like a train.

Shells are named with letters:

Shell	Shell number
$\mathrm{K}$	$n = 1$
$\mathrm{L}$	$n = 2$
$\mathrm{M}$	$n = 3$
$\mathrm{N}$	$n = 4$
$\mathrm{O}$	$n = 5$
$\mathrm{P}$	$n = 6$
$\mathrm{Q}$	$n = 7$

The letters $\mathrm{K}$ through $\mathrm{Q}$ are shell names. The value $n$ is the shell number. A larger $n$ means a farther energy level.

Maximum Electron Capacity

The maximum number of electrons in one shell is calculated with:

\text{maximum electrons in a shell} = 2n^2

LibreTexts explains the shell names $\mathrm{K}$ through $\mathrm{Q}$ and their maximum capacities in its Bohr model discussion. The reference is available at chem.libretexts.org.

The results are:

Shell	Shell number	Maximum electrons from $2n^2$
$\mathrm{K}$	$1$	$2(1)^2 = 2$
$\mathrm{L}$	$2$	$2(2)^2 = 8$
$\mathrm{M}$	$3$	$2(3)^2 = 18$
$\mathrm{N}$	$4$	$2(4)^2 = 32$
$\mathrm{O}$	$5$	$2(5)^2 = 50$
$\mathrm{P}$	$6$	$2(6)^2 = 72$
$\mathrm{Q}$	$7$	$2(7)^2 = 98$

The word maximum matters. Shell $\mathrm{M}$ can hold up to $18$ electrons, but that does not mean every atom fills $\mathrm{M}$ to $18$ before using the next shell. For introductory examples up to calcium, we use the simpler pattern in the interactive lab.

Shell Lab for Light Elements

Choose a neutral atom. Notice that the electron count equals the atomic number, then read how the electrons are distributed across shells $\mathrm{K}$ , $\mathrm{L}$ , $\mathrm{M}$ , and $\mathrm{N}$ .

Atomic Shell Model

This diagram uses the simple shell model for neutral atoms up to calcium. It focuses on reading the outer shell and separating the shell content from the maximum

2n^2

capacity.

Calcium has $20$ electrons, so its simple shell pattern is $2, 8, 8, 2$ .

Atomic number: $Z = 20$
Configuration: $2, 8, 8, 2$
Outer shell: $\mathrm{N}$
capacity: $2(4)^2 = 32$

Why Calcium Is Two Eight Eight Two

Calcium has atomic number $20$ . The symbol $Z$ means atomic number. Since the atom is neutral, it also has $20$ electrons.

Calcium Shell Filling Steps

The filling steps in the simple shell model are:

\begin{aligned} \mathrm{Ca}: Z &= 20 \\ e^- &= 20 \\ \mathrm{K} &: 2 \quad \text{left } 18 \\ \mathrm{L} &: 8 \quad \text{left } 10 \\ \mathrm{M} &: 8 \quad \text{left } 2 \\ \mathrm{N} &: 2 \quad \text{left } 0 \end{aligned}

Why Not Two Eight Ten

A common question is: why not $2, 8, 10$ ?

The answer is that in the simple shell model for light elements up to calcium, shell $\mathrm{M}$ is written with $8$ electrons before the remaining electrons begin shell $\mathrm{N}$ . After shells $\mathrm{K}$ and $\mathrm{L}$ are filled, calcium has $10$ electrons left, so shell $\mathrm{M}$ is written as $8$ and shell $\mathrm{N}$ receives the remaining $2$ .

Therefore:

\text{calcium electron configuration} = 2, 8, 8, 2

Limits of the Model

Do not mix up these two ideas.

Statement	Accurate meaning
Atomic shells are drawn as circles.	The drawing helps show energy levels. It is not a rigid physical path.
The formula $2n^2$ gives maximum capacity.	It is not the complete filling order for every element. Heavier elements need the subshell and orbital model.

OpenStax explains that in the modern orbital model, electrons after argon enter the $4s$ level before $3d$ . The reference is available at openstax.org. Here, we stop at the simple shell pattern so the foundation stays clear.

The outermost shell also leads into the idea of valence electrons. Electrons in the outermost shell are called valence electrons, and they strongly affect whether an atom tends to form ions or chemical bonds.