KAHIBARO
Table of Contents
Filling electron states in atoms
Electron configuration tells us how the electrons of an atom are arranged among available atomic states. It is a compact way to describe the structure of an atom and helps explain chemical behavior, periodic trends, and many spectral properties.
A neutral atom has as many electrons as its atomic number $Z$. These electrons do not all sit at the same distance from the nucleus. Instead, they occupy allowed states organized into shells and subshells. Since orbitals and electron shells are covered elsewhere in the course, here the focus is on how electrons are assigned to those available places.
The basic filling idea
When writing an electron configuration, we place electrons into orbitals starting from lower energy states and moving to higher energy states. For many atoms, especially in their ground state, this produces the most stable arrangement.
Each subshell is labeled by a number and a letter, such as $1s$, $2p$, or $3d$. The number gives the principal shell, and the letter gives the subshell type. Different subshells can hold different maximum numbers of electrons.
The capacities are:
| Subshell | Number of orbitals | Maximum electrons |
|---|---|---|
| $s$ | 1 | 2 |
| $p$ | 3 | 6 |
| $d$ | 5 | 10 |
| $f$ | 7 | 14 |
This follows because each orbital can hold at most two electrons.
Each orbital can contain at most two electrons, and those two electrons must have opposite spins.
Rules used to build configurations
Three main rules are used to write ground state electron configurations.
The first is the Aufbau principle. Electrons fill lower energy orbitals before higher energy ones.
The second is the Pauli exclusion principle. No two electrons in the same atom can have the same full set of quantum numbers. In practice, this means one orbital holds at most two electrons with opposite spins.
The third is Hund's rule. When orbitals of the same energy are available, such as the three $p$ orbitals, electrons occupy them one at a time with parallel spins before pairing up.
Ground state configurations are built using three key ideas: fill lowest energy first, allow at most two electrons per orbital, and spread electrons singly across equal energy orbitals before pairing.
Order of filling
A useful practical order for filling subshells is:
$$
1s,\ 2s,\ 2p,\ 3s,\ 3p,\ 4s,\ 3d,\ 4p,\ 5s,\ 4d,\ 5p,\ 6s,\ 4f,\ 5d,\ 6p,\ 7s,\ 5f,\ 6d,\ 7p
$$
This order is based on orbital energies in many-electron atoms. It is not the same as simply increasing the principal quantum number.
A common diagram for remembering the order is the diagonal rule.
Writing electron configurations
A full electron configuration lists all occupied subshells and the number of electrons in each one. The superscript gives the number of electrons.
For example, hydrogen, with $Z=1$, has
$$
1s^1
$$
Helium, with $Z=2$, has
$$
1s^2
$$
Lithium, with $Z=3$, starts a new subshell:
$$
1s^2\,2s^1
$$
Carbon, with $Z=6$, is
$$
1s^2\,2s^2\,2p^2
$$
Oxygen, with $Z=8$, is
$$
1s^2\,2s^2\,2p^4
$$
Calcium, with $Z=20$, is
$$
1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2
$$
Orbital box pictures
Sometimes electron configurations are shown with boxes or lines for orbitals and arrows for spins. This makes Hund's rule easy to see.
For carbon, the $2p^2$ part is arranged as two unpaired electrons in separate $p$ orbitals.
For oxygen, the $2p^4$ part has one paired orbital and two singly occupied orbitals.
Noble gas shorthand
For larger atoms, writing the full configuration becomes long. A shorter notation uses the nearest previous noble gas in brackets.
For sodium, the full configuration is
$$
1s^2\,2s^2\,2p^6\,3s^1
$$
Since $1s^2\,2s^2\,2p^6$ is the configuration of neon, we write
$$
[\mathrm{Ne}]\,3s^1
$$
For calcium,
$$
[\mathrm{Ar}]\,4s^2
$$
For iron,
$$
[\mathrm{Ar}]\,4s^2\,3d^6
$$
This shorthand is very useful because the inner closed shells often do not change much in ordinary atomic behavior.
Configurations and the periodic table
Electron configurations follow the structure of the periodic table. Elements in the same column often have similar outer electron arrangements, which helps explain similar chemical properties.
The table can be divided into blocks according to the subshell being filled.
| Block | Last subshell being filled | Example |
|---|---|---|
| $s$ block | $ns$ | Na, Mg |
| $p$ block | $np$ | O, Cl |
| $d$ block | $(n-1)d$ | Fe, Cu |
| $f$ block | $(n-2)f$ | Ce, U |
This is why the shape of the periodic table reflects atomic structure.
Valence electrons
The most chemically important electrons are usually the outermost ones, called valence electrons. Electron configurations help us identify them.
For main-group elements, valence electrons are often the electrons in the highest principal shell. For example, sulfur has
$$
1s^2\,2s^2\,2p^6\,3s^2\,3p^4
$$
Its valence electrons are the six electrons in the $n=3$ shell, so sulfur has 6 valence electrons.
Valence electrons are central for bonding and chemical reactivity, but those topics belong more to chemistry. Here it is enough to note that electron configuration makes them visible.
Exceptions to simple filling
The simple filling order works well, but some atoms are exceptions because very close energy levels can swap order slightly. A well-known example is chromium.
A naive filling would suggest
$$
[\mathrm{Ar}]\,4s^2\,3d^4
$$
but the observed ground state is
$$
[\mathrm{Ar}]\,4s^1\,3d^5
$$
Copper is another example. Instead of
$$
[\mathrm{Ar}]\,4s^2\,3d^9
$$
the observed configuration is
$$
[\mathrm{Ar}]\,4s^1\,3d^{10}
$$
These exceptions occur because half-filled and fully filled subshells can be especially stable.
Do not assume the simple filling order is exact for every atom. Chromium and copper are classic exceptions:
$$
\mathrm{Cr}: [\mathrm{Ar}]\,4s^1\,3d^5
$$
$$
\mathrm{Cu}: [\mathrm{Ar}]\,4s^1\,3d^{10}
$$
Electron configurations of ions
When atoms gain or lose electrons, they form ions. The electron configuration changes accordingly.
A cation is formed by removing electrons. For main-group elements, electrons are usually removed from the highest principal shell first.
For example, sodium is
$$
[\mathrm{Ne}]\,3s^1
$$
So sodium ion is
$$
\mathrm{Na}^+ : [\mathrm{Ne}]
$$
For transition metals, care is needed. Although $4s$ often fills before $3d$, electrons are usually removed from $4s$ before $3d$ once the atom is ionized.
For iron,
$$
\mathrm{Fe}: [\mathrm{Ar}]\,4s^2\,3d^6
$$
Then
$$
\mathrm{Fe}^{2+}: [\mathrm{Ar}]\,3d^6
$$
and
$$
\mathrm{Fe}^{3+}: [\mathrm{Ar}]\,3d^5
$$
Anions are formed by adding electrons to available states. For chlorine,
$$
\mathrm{Cl}: [\mathrm{Ne}]\,3s^2\,3p^5
$$
so
$$
\mathrm{Cl}^-: [\mathrm{Ne}]\,3s^2\,3p^6 = [\mathrm{Ar}]
$$
Examples
A few examples show the process clearly.
For nitrogen, $Z=7$. Fill in order:
$$
1s^2\,2s^2\,2p^3
$$
The three $2p$ electrons occupy separate $p$ orbitals first.
For magnesium, $Z=12$:
$$
1s^2\,2s^2\,2p^6\,3s^2 = [\mathrm{Ne}]\,3s^2
$$
For potassium, $Z=19$:
$$
[\mathrm{Ar}]\,4s^1
$$
For zinc, $Z=30$:
$$
[\mathrm{Ar}]\,4s^2\,3d^{10}
$$
The following table summarizes some common cases.
| Element | Atomic number $Z$ | Electron configuration |
|---|---|---|
| H | 1 | $1s^1$ |
| He | 2 | $1s^2$ |
| C | 6 | $1s^2\,2s^2\,2p^2$ |
| N | 7 | $1s^2\,2s^2\,2p^3$ |
| O | 8 | $1s^2\,2s^2\,2p^4$ |
| Na | 11 | $[\mathrm{Ne}]\,3s^1$ |
| Mg | 12 | $[\mathrm{Ne}]\,3s^2$ |
| Cl | 17 | $[\mathrm{Ne}]\,3s^2\,3p^5$ |
| K | 19 | $[\mathrm{Ar}]\,4s^1$ |
| Ca | 20 | $[\mathrm{Ar}]\,4s^2$ |
| Fe | 26 | $[\mathrm{Ar}]\,4s^2\,3d^6$ |
| Cu | 29 | $[\mathrm{Ar}]\,4s^1\,3d^{10}$ |
Why electron configurations matter
Electron configurations connect atomic structure to observable behavior. They help explain why the periodic table has its pattern, why some elements are reactive and others are not, why ions form in particular ways, and why certain spectral lines appear.
They are also the starting point for understanding atomic magnetism. Atoms with unpaired electrons often behave differently from atoms whose electrons are all paired.
Electron configuration is the organized distribution of an atom's electrons among shells, subshells, and orbitals. It is determined mainly by the lowest-energy arrangement together with the Pauli exclusion principle and Hund's rule.
Final perspective
Electron configurations are a practical language for describing atoms. Once the available subshells are known, the main task is to count electrons and place them in the correct order while following the filling rules. With practice, the notation becomes a quick and powerful way to read atomic structure directly from the periodic table.