The electron configuration of an atom describes how its electrons are distributed among atomic orbitals. In introductory
chemistry and atomic physics, the ground-state configuration is built by combining three central ideas: the
Pauli exclusion principle, the Aufbau principle, and Hund’s rule. Together, they explain why
electrons occupy orbitals in a particular pattern and why some atoms have unpaired electrons while others do not.
Pauli exclusion principle
The Pauli exclusion principle states that no two electrons in the same atom can have the same complete set of quantum
numbers. In orbital language, this means that a single orbital can hold at most two electrons, and if two electrons
occupy the same orbital, they must have opposite spins.
Maximum occupancy of an orbital.
\[
\begin{aligned}
\text{one orbital} &\rightarrow 2 \text{ electrons}
\end{aligned}
\]
Since each subshell contains several orbitals, its total capacity depends on the orbital angular momentum quantum number
\(l\). The number of orbitals in a subshell is \(2l+1\), so the maximum number of electrons is
Subshell capacity formula.
\[
\begin{aligned}
N_{\max} &= 2(2l+1)
\end{aligned}
\]
This gives the familiar capacities:
| Subshell |
\(l\) |
Orbitals |
Maximum electrons |
| s |
0 |
1 |
2 |
| p |
1 |
3 |
6 |
| d |
2 |
5 |
10 |
| f |
3 |
7 |
14 |
Aufbau principle
The Aufbau principle says that electrons fill lower-energy orbitals before higher-energy ones. In school-level electron
configuration work, this leads to the common filling order
Typical Aufbau sequence.
\[
\begin{aligned}
1s &\rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 5s \rightarrow \cdots
\end{aligned}
\]
This order is not simply a straight increase in \(n\), because subshell energies overlap. For example, the \(4s\)
subshell is filled before \(3d\) in the usual ground-state Aufbau sequence.
| Early filling sequence |
Meaning |
| 1s, 2s, 2p, 3s, 3p |
Builds the configurations up to argon |
| 4s, 3d, 4p |
Explains the first transition-metal period and p-block extension |
| 5s, 4d, 5p |
Continues through the next main period |
| 6s, 4f, 5d, 6p |
Introduces lanthanides and the next transition block |
| 7s, 5f, 6d, 7p |
Extends to very heavy atoms |
Hund’s rule
Hund’s rule applies when several orbitals have the same energy, such as the three orbitals of a p subshell or the five
orbitals of a d subshell. It says that electrons occupy these orbitals singly first, with parallel spins, before any
pairing occurs.
Hund filling idea.
\[
\begin{aligned}
\uparrow\ \uparrow\ \uparrow \quad \text{before} \quad \uparrow\downarrow
\end{aligned}
\]
This is why partially filled p and d subshells often produce several unpaired electrons. Those unpaired electrons are
important because they influence magnetic behavior. Atoms with one or more unpaired electrons are typically
paramagnetic, while atoms with all electrons paired are typically diamagnetic.
Noble-gas shorthand
For larger atoms, writing the full configuration can be long. Chemists therefore use a noble-gas core notation. The
configuration of the previous noble gas is placed in brackets, and only the remaining outer subshells are written
explicitly. For example, iron can be written as
Full and shorthand notation for iron.
\[
\begin{aligned}
\text{full} &:\ 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^6 \\
\text{shorthand} &:\ [\mathrm{Ar}]\,4s^2\,3d^6
\end{aligned}
\]
The bracketed core stands for all electrons belonging to the noble-gas configuration. This makes it easier to focus on
the chemically important outer subshells.
Sample example: iron, \(Z=26\)
Iron has 26 electrons in its neutral ground state. Fill them in the usual order:
Step 1. Fill the low-energy subshells up to argon.
\[
\begin{aligned}
1s^2\,2s^2\,2p^6\,3s^2\,3p^6 &= 18 \text{ electrons} = [\mathrm{Ar}]
\end{aligned}
\]
After reaching the argon core, 8 electrons remain.
Step 2. Continue with the next subshells in Aufbau order.
\[
\begin{aligned}
4s^2 &\rightarrow \text{uses 2 more electrons} \\
3d^6 &\rightarrow \text{uses the remaining 6 electrons}
\end{aligned}
\]
So the configuration becomes
Final iron configuration.
\[
\begin{aligned}
[\mathrm{Ar}]\,4s^2\,3d^6
\end{aligned}
\]
Now apply Hund’s rule to the \(3d^6\) subshell. The five d orbitals fill singly first, and only then does pairing
begin. That means the six d electrons are distributed so that four remain unpaired:
Unpaired electrons in \(3d^6\).
\[
\begin{aligned}
3d^6 &\rightarrow 4 \text{ unpaired electrons}
\end{aligned}
\]
Therefore iron is paramagnetic in this ground-state picture.
Ground-state exceptions
In more advanced chemistry, some atoms do not follow the naive Aufbau order exactly. Chromium and copper are famous
examples. Chromium is usually written as \([\mathrm{Ar}]\,4s^1\,3d^5\) rather than \([\mathrm{Ar}]\,4s^2\,3d^4\), and
copper is usually written as \([\mathrm{Ar}]\,4s^1\,3d^{10}\) rather than \([\mathrm{Ar}]\,4s^2\,3d^9\). These
exceptions arise because half-filled or fully filled d subshells can be especially stable.
At university level, one also studies excited configurations, ion configurations, spin states, exchange energy,
shielding, and more refined quantum-mechanical explanations. However, for most school and early undergraduate work, the
combination of Pauli exclusion, Aufbau filling, and Hund’s rule provides the standard and most useful way to build
ground-state electron configurations.
| Principle |
Main idea |
Practical result |
| Pauli exclusion |
At most two opposite-spin electrons per orbital |
Controls pairing inside each box |
| Aufbau principle |
Lower-energy subshells fill before higher-energy ones |
Generates the standard filling order |
| Hund’s rule |
Equal-energy orbitals fill singly before pairing |
Determines the number of unpaired electrons |
| Noble-gas shorthand |
Replace inner electrons with a bracketed noble-gas core |
Shortens long configurations |
| Magnetic behavior |
Unpaired electrons lead to paramagnetism |
Links configuration to observable properties |