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.

The Bohr model uses orbits with specific energies to explain the line spectrum of hydrogen.

In a shell diagram, each circle marks an energy level. The circles are not solid paths followed by electrons. They only show the arrangement of energy levels in the simple model.

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. As $n$ increases, the electron shell is generally farther from the nucleus and has higher energy.

Maximum Electron Capacity

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

For shell number $n$ , the maximum number of electrons is $2n^2$ .

The shells are named $\mathrm{K}$ through $\mathrm{Q}$ , and each has a maximum capacity.

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 the examples up to calcium, we use the simpler pattern in the interactive model.

Shell Model 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: $2(4)^2 = 32$

Calcium Electron Configuration

Calcium has atomic number $20$ . The symbol $Z$ means atomic number. Since the atom is neutral, it also has $20$ electrons. Fill the shells in order from the lowest energy, and record the electron count of each shell as you go.

Calcium Shell Filling Steps

In the simple shell model, calcium's shells fill in this order:

\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}

Filling Shells M and N

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 $2$ .

The calculation gives:

The electron configuration of calcium is $2,8,8,2$ .

Limits of the Model

Do not mix up these two ideas.

Statement	Accurate meaning
Atomic shells are drawn as circles.	The drawing represents energy levels. Electrons do not follow a rigid circular path.
The formula $2n^2$ gives maximum capacity.	Maximum capacity differs from the order in which electrons fill the shells. Heavier elements need the subshell and orbital model.

In the modern orbital model, electrons after argon fill $4s$ before $3d$ . The interactive model above uses a simple shell pattern to show the number of electrons in each shell. A more detailed configuration uses the modern orbital-filling order.

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.