6.1 · Periodic properties

Electron configurations

Filling orbitals in order of energy: aufbau, Pauli and Hund, plus the Cr and Cu exceptions.

By the end you should be able to:

Write ground-state electron configurations and orbital diagrams (aufbau, Hund, Pauli, Cr and Cu exceptions)

Interactive

Electron configuration builder

Fill orbital boxes for any atom or ion, with live checks for the Pauli principle, Hund's rule and aufbau order.

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Key idea

Aufbau, Pauli and Hund

Three rules give the ground-state configuration of an atom:

Aufbau: electrons fill the lowest-energy subshell available first.
Pauli exclusion: no two electrons in an atom have the same four quantum numbers, so an orbital holds at most two electrons, with opposite spins ( $m_s = +\tfrac12$ and $-\tfrac12$ ).
Hund's rule: in a set of degenerate orbitals (the three $2p$ , the five $3d$ ), electrons occupy separate orbitals with parallel spins before any orbital receives a second electron.

A configuration lists each subshell with its electron count as a superscript: nitrogen is $1s^2\,2s^2\,2p^3$ , with three unpaired $2p$ electrons.

Formula

Filling order and subshell capacity

A subshell with angular momentum quantum number $l$ has $2l+1$ orbitals, so it holds $2(2l+1)$ electrons: s holds 2, p holds 6, d holds 10, f holds 14.

Subshells fill in order of increasing $n + l$ ; for equal $n + l$ the lower $n$ fills first:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p

So $4s$ ( $n + l = 4$ ) fills before $3d$ ( $n + l = 5$ ). The periodic table encodes the same order: reading across, the s block is 2 elements wide, the p block 6, the d block 10 and the f block 14.

Method

Writing a configuration and an orbital diagram

Count the electrons: $Z$ for a neutral atom.
Fill subshells in aufbau order, filling each completely before starting the next (Cr and Cu are the exceptions).
For noble-gas notation, replace the core with the preceding noble gas in brackets: iron is $[\mathrm{Ar}]\,4s^2\,3d^6$ .
For an orbital diagram, draw one box per orbital. In a partly filled subshell, put one electron in each box with parallel spins (Hund) before pairing any (Pauli).
Check that the superscripts add up to the electron count.

Writing $[\mathrm{Ar}]\,3d^6\,4s^2$ (ordered by $n$ ) describes the same configuration as $[\mathrm{Ar}]\,4s^2\,3d^6$ .

Key idea

The Cr and Cu exceptions

Chromium and copper move one $4s$ electron into $3d$ , giving a half-filled or completely filled d subshell:

Atom	Predicted by aufbau	Actual ground state
$\ce{Cr}$ ( $Z = 24$ )	$[\mathrm{Ar}]\,4s^2\,3d^4$	$[\mathrm{Ar}]\,4s^1\,3d^5$
$\ce{Cu}$ ( $Z = 29$ )	$[\mathrm{Ar}]\,4s^2\,3d^9$	$[\mathrm{Ar}]\,4s^1\,3d^{10}$

The $4s$ and $3d$ subshells are close in energy, and the half-filled $3d^5$ and filled $3d^{10}$ arrangements are especially stable. Chromium therefore has 6 unpaired electrons (one in $4s$ , five in $3d$ ) and copper has 1. The elements below them do the same: molybdenum is $[\mathrm{Kr}]\,5s^1\,4d^5$ and silver is $[\mathrm{Kr}]\,5s^1\,4d^{10}$ .

Common mistake

Common configuration mistakes

Wrong: Cr is $[\mathrm{Ar}]\,4s^2\,3d^4$ . Right: $[\mathrm{Ar}]\,4s^1\,3d^5$ ; likewise Cu is $[\mathrm{Ar}]\,4s^1\,3d^{10}$ , not $4s^2\,3d^9$ .
Wrong: $2p^3$ drawn as (↑↓)(↑)( ). Right: (↑)(↑)(↑): three unpaired electrons in separate orbitals with parallel spins (Hund).
Wrong: potassium is $[\mathrm{Ar}]\,3d^1$ . Right: $[\mathrm{Ar}]\,4s^1$ ; $4s$ fills before $3d$ , and $3d$ first gains an electron at scandium.
Wrong: putting three electrons in one orbital to "finish" a subshell. Right: an orbital never holds more than two electrons (Pauli).

Worked example

Worked example: sulfur and iron

Sulfur, Z = 16. Filling in order: $1s^2\,2s^2\,2p^6\,3s^2\,3p^4$ , or $[\mathrm{Ne}]\,3s^2\,3p^4$ . Valence orbital diagram:

$3s$	$3p$	$3p$	$3p$
↑↓	↑↓	↑	↑

The fourth $3p$ electron must pair, leaving 2 unpaired electrons.

Iron, Z = 26. $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^6$ , or $[\mathrm{Ar}]\,4s^2\,3d^6$ . Five $3d$ electrons go in singly and the sixth pairs:

$3d$	$3d$	$3d$	$3d$	$3d$
↑↓	↑	↑	↑	↑

Iron has 4 unpaired electrons.

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