The electronic structure of a polyelectronic atom is summarized by its electronic configuration, which specifies how electrons occupy atomic orbitals. These configurations are built using the Aufbau principle, together with the Pauli Exclusion Principle and Hund’s rules.
The Aufbau principle
The Aufbau principle states that electrons occupy available orbitals in order of increasing energy. For polyelectronic atoms, orbital energies depend on both the principal quantum number \(n\) and the orbital angular momentum quantum number \(l\), leading to an ordering such as
\[ 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p \;\cdots \]
Each orbital can hold at most two electrons with opposite spins.
Subshell labels and \(l\) values
Atomic subshells are labeled by letters that correspond to specific values of the orbital angular momentum quantum number:
| Subshell | \(l\) value |
|---|---|
| \(s\) | 0 |
| \(p\) | 1 |
| \(d\) | 2 |
| \(f\) | 3 |
These values determine the shape of the orbitals and play a central role in angular momentum coupling and atomic term symbols.
Example electronic configurations
Carbon (\(Z=6\)):
\[ \mathrm{C}: 1s^2\,2s^2\,2p^2 \]
Carbon has two electrons in the \(2p\) subshell (\(l=1\)), which leads to multiple possible term symbols depending on how the spins and angular momenta combine.
Nickel (\(Z=28\)):
\[ \mathrm{Ni}: [\mathrm{Ar}]\,4s^2\,3d^8 \]
In nickel, electrons occupy both \(s\) and \(d\) subshells. The partially filled \(3d\) subshell (\(l=2\)) is responsible for the rich term structure and spectroscopy of transition metals.
Important exceptions: half-filled and filled \(d\) subshells
While the Aufbau principle correctly predicts most electronic configurations, there are notable exceptions among the transition metals. In particular, atoms such as chromium and copper (and their heavier analogs molybdenum and silver) adopt configurations that differ from the naive Aufbau ordering.
In these cases, one electron is promoted from an \(s\) subshell into a \(d\) subshell, producing a half-filled or completely filled \(d\) subshell.
Representative examples are:
\[ \begin{aligned} \mathrm{Cr}:&\ [\mathrm{Ar}]\,4s^1\,3d^5 \quad (\text{instead of } 4s^2\,3d^4),\\ \mathrm{Cu}:&\ [\mathrm{Ar}]\,4s^1\,3d^{10} \quad (\text{instead of } 4s^2\,3d^9),\\ \mathrm{Mo}:&\ [\mathrm{Kr}]\,5s^1\,4d^5,\\ \mathrm{Ag}:&\ [\mathrm{Kr}]\,5s^1\,4d^{10}. \end{aligned} \]
These configurations are more stable because half-filled and filled \(d\) subshells benefit from:
- increased exchange stabilization,
- reduced electron–electron repulsion within the subshell,
- a favorable balance between \(s\) and \(d\) orbital energies.
Although these exceptions violate the simplest application of the Aufbau principle, they are fully consistent with the underlying quantum-mechanical energetics of the atom.
Big idea: small energy differences between \(s\) and \(d\) orbitals allow electron rearrangements that favor particularly stable half-filled or filled subshells.
Big idea: electronic configurations provide the starting point for understanding atomic structure, term symbols, and spectra by specifying how electrons populate subshells with different angular momenta.
Periodic table organized by subshell filling
The periodic table can be understood as a map showing how electrons fill atomic subshells according to the Aufbau principle. Elements are grouped into blocks based on the type of orbital being filled by the outermost electrons.
| s-block | d-block | p-block | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| H | He | ||||||||||||||||
| Li | Be | B | C | N | O | F | Ne | ||||||||||
| Na | Mg | Sc | Ti | V | Cr | Mn | Fe | Co | Ni | Cu | Zn | Al | Si | P | S | Cl | Ar |
| K | Ca | Y | Zr | Nb | Mo | Tc | Ru | Rh | Pd | Ag | Cd | Ga | Ge | As | Se | Br | Kr |
| Rb | Sr | In | Sn | Sb | Te | I | Xe | ||||||||||
f-block (inner transition elements)
| La | Ce | Pr | Nd | Pm | Sm | Eu | Gd | Tb | Dy | Ho | Er | Tm | Yb | Lu |
| Ac | Th | Pa | U | Np | Pu | Am | Cm | Bk | Cf | Es | Fm | Md | No | Lr |
Block interpretation
- s-block: filling of \(ns\) orbitals
- p-block: filling of \(np\) orbitals
- d-block: filling of \( (n-1)d \) orbitals
- f-block: filling of \( (n-2)f \) orbitals
This block structure explains trends in electronic configurations and helps predict which subshells are partially filled—information that is essential for determining atomic term symbols and spectroscopic behavior.
Big idea: the periodic table is a visual summary of subshell filling, organizing elements according to the quantum numbers of their valence electrons.