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Learn atomic shells as electron energy levels, shell numbers, the 2n^2 capacity rule, and the calcium shell configuration.

---

## 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 [The Bohr Model from OpenStax](https://openstax.org/books/chemistry-atoms-first-2e/pages/3-2-the-bohr-model).

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

Visible text: | Shell | Shell number |
| :---- | :----------- |
| | |
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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.

Visible text: The letters through are shell names. The value is the **shell number**. A larger means a farther energy level.

## Maximum Electron Capacity

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

```math
\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 [The Bohr Model of Atoms from LibreTexts](https://chem.libretexts.org/Courses/Barstow_Community_College/Survey_of_Chemistry_and_Physics/2%3A_Structure_of_Matter/3%3A_Atomic_Theory/2.4%3A_Atomic_Structure/2.3.5%3A_The_Bohr_Model_of_Atoms).

Visible text: LibreTexts explains the shell names through and their maximum capacities in its Bohr model discussion. The reference is available at [The Bohr Model of Atoms from LibreTexts](https://chem.libretexts.org/Courses/Barstow_Community_College/Survey_of_Chemistry_and_Physics/2%3A_Structure_of_Matter/3%3A_Atomic_Theory/2.4%3A_Atomic_Structure/2.3.5%3A_The_Bohr_Model_of_Atoms).

The results are:

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

Visible text: | Shell | Shell number | Maximum electrons from |
| :---- | :----------- | :----------------------------------------------- |
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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.

Visible text: The word **maximum** matters. Shell can hold up to electrons, but that does not mean every atom fills to 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 $$\mathrm{N}$$.

Visible text: Choose a neutral atom. Notice that the electron count equals the atomic number, then read how the electrons are distributed across shells , , , and .

Component: AtomShellLab
Props:
- title: Atomic Shell Model
- description: 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.
  Visible text: 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 capacity.
- labels: {
chooseAtom: "Choose a neutral atom",
atomicNumber: "Atomic number",
configuration: "Configuration",
electronTotal: "Electron count",
maximumCapacity: "capacity",
outerShell: "Outer shell",
samples: {
neon: {
tab: "Ne",
name: "Neon",
note: <>Its configuration is $$2, 8$$. Shell $$\mathrm{L}$$ is the outer shell.</>,
},
magnesium: {
tab: "Mg",
name: "Magnesium",
note: <>After shells $$\mathrm{K}$$ and $$\mathrm{L}$$ are filled, the remaining $$2$$ electrons enter shell $$\mathrm{M}$$.</>,
},
chlorine: {
tab: "Cl",
name: "Chlorine",
note: <>Its outer shell contains $$7$$ electrons in this simple shell model.</>,
},
argon: {
tab: "Ar",
name: "Argon",
note: <>The introductory pattern is $$2, 8, 8$$, so shell $$\mathrm{M}$$ contains $$8$$ electrons.</>,
},
potassium: {
tab: "K",
name: "Potassium",
note: <>Potassium has the element symbol $$\mathrm{K}$$. That is different from shell $$\mathrm{K}$$. After $$2, 8, 8$$, the remaining $$1$$ electron enters shell $$\mathrm{N}$$.</>,
},
calcium: {
tab: "Ca",
name: "Calcium",
note: <>Calcium has $$20$$ electrons, so its simple shell pattern is $$2, 8, 8, 2$$.</>,
},
},
}
  Visible text: {
chooseAtom: "Choose a neutral atom",
atomicNumber: "Atomic number",
configuration: "Configuration",
electronTotal: "Electron count",
maximumCapacity: "capacity",
outerShell: "Outer shell",
samples: {
neon: {
tab: "Ne",
name: "Neon",
note: <>Its configuration is . Shell is the outer shell.</>,
},
magnesium: {
tab: "Mg",
name: "Magnesium",
note: <>After shells and are filled, the remaining electrons enter shell .</>,
},
chlorine: {
tab: "Cl",
name: "Chlorine",
note: <>Its outer shell contains electrons in this simple shell model.</>,
},
argon: {
tab: "Ar",
name: "Argon",
note: <>The introductory pattern is , so shell contains electrons.</>,
},
potassium: {
tab: "K",
name: "Potassium",
note: <>Potassium has the element symbol . That is different from shell . After , the remaining electron enters shell .</>,
},
calcium: {
tab: "Ca",
name: "Calcium",
note: <>Calcium has electrons, so its simple shell pattern is .</>,
},
},
}

## 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.

Visible text: Calcium has atomic number . The symbol means atomic number. Since the atom is neutral, it also has electrons.

### Calcium Shell Filling Steps

The filling steps in the simple shell model are:

```math
\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 $$2, 8, 10$$?

Visible text: A common question is: why not ?

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 $$2$$.

Visible text: The answer is that in the simple shell model for light elements up to calcium, shell is written with electrons before the remaining electrons begin shell . After shells and are filled, calcium has electrons left, so shell is written as and shell receives the remaining .

Therefore:

```math
\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. |

Visible text: | Statement | Accurate meaning |
| :-------- | :--------------- |
| Atomic shells are drawn as circles. | The drawing helps show energy levels. It is not a rigid physical path. |
| The formula 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 [Electronic Structure of Atoms from OpenStax](https://openstax.org/books/chemistry/pages/6-4-electronic-structure-of-atoms-electron-configurations). Here, we stop at the simple shell pattern so the foundation stays clear.

Visible text: OpenStax explains that in the modern orbital model, electrons after argon enter the level before . The reference is available at [Electronic Structure of Atoms from OpenStax](https://openstax.org/books/chemistry/pages/6-4-electronic-structure-of-atoms-electron-configurations). 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.