# Electron configurations

> IB Chemistry HL · S1: Models of the particulate nature of matter
> Source: https://www.owlsprep.com/study/ib-chemistry-hl-u1-electron-configurations/

This sub-topic covers how electrons are arranged in atomic orbitals, following three core rules. You will learn to write full and condensed electron configurations for atoms and monatomic ions, and understand common exceptions to expected patterns.

**Prerequisites:** [Atomic orbitals and energy levels](https://www.owlsprep.com/study/ib-chemistry-hl-u1-atomic-orbitals/); [Quantum numbers for electrons](https://www.owlsprep.com/study/ib-chemistry-hl-u1-quantum-numbers/)

## Learning objectives

- Write full and condensed electron configurations for neutral atoms and monatomic ions
- Apply Aufbau principle, Hund's rule and Pauli exclusion principle correctly
- Explain common exceptions to expected electron configurations for transition metals
- Interpret orbital diagrams and identify unpaired electrons

## Core Rules for Electron Filling

**Pauli Exclusion Principle** — No two electrons in the same atom can have an identical set of four quantum numbers. This means each orbital can hold a maximum of two electrons with opposite spin.

*Example:* A 1s orbital can hold 2 electrons with opposite spin, but cannot hold 3 electrons.

Three core rules govern how electrons fill orbitals in the ground state (lowest energy state) of an atom:

- **Aufbau Principle**: Electrons fill lower energy orbitals before higher energy orbitals. Energy is determined by the $n+l$ rule: lower $n+l$ = lower energy; for equal $n+l$, lower $n$ fills first.
- **Hund's Rule**: When filling degenerate (equal energy) orbitals, electrons fill them singly first with parallel spins, before pairing up. This minimizes electron-electron repulsion.

**Worked example:** Draw the orbital filling diagram and write the electron configuration for a neutral nitrogen atom (atomic number = 7)

1. Calculate total number of electrons: for neutral N, $Z=7$, so 7 electrons total.
2. Apply filling order: 1s < 2s < 2p. Fill lower energy orbitals first: 2 electrons in 1s, 2 electrons in 2s, leaving 3 electrons for 2p.
3. Apply Hund's rule to the three degenerate 2p orbitals: place one unpaired electron in each orbital with parallel spin.
4. $$1s^2 2s^2 2p^3$$

> **tip**
>
> Always mark parallel unpaired spins when drawing orbital diagrams; exam markers award specific marks for this detail.

## Full and Condensed Electron Configurations

Full electron configurations list every occupied subshell with its electron count, ordered by principal quantum number $n$. Condensed (noble gas core) configurations replace the electron configuration of the nearest preceding noble gas with its symbol in square brackets, only showing outer valence electrons.

**Worked example:** Write the full and condensed electron configuration for neutral calcium (Z = 20)

1. Neutral calcium has 20 electrons total. Fill orbitals in order of increasing energy: 1s → 2s → 2p → 3s → 3p → 4s.
2. $$1s^2 2s^2 2p^6 3s^2 3p^6 4s^2$$
3. Find the nearest noble gas that comes before calcium: argon (Z = 18), which has the configuration $1s^2 2s^2 2p^6 3s^2 3p^6$.
4. $$\text{Condensed configuration: } [Ar] 4s^2$$

> **warning**
>
> The order of writing subshells in the final configuration is ordered by $n$, not filling order. For example, after filling 4s before 3d, you must write 3d before 4s in the final configuration.

## Electron Configurations of Ions

For charged ions, the total number of electrons changes: add one electron for each negative charge, subtract one for each positive charge. A critical rule for transition metal cations: $ns$ electrons are lost before $(n-1)d$ electrons when ions form.

**Worked example:** Write the condensed electron configuration for Fe³⁺ (iron(III) ion, Z = 26 for Fe)

1. First write the configuration for neutral iron, with 26 electrons.
2. $$Fe: [Ar] 3d^6 4s^2$$
3. Fe³⁺ has lost 3 electrons total. Remove 4s electrons first, as they are higher in energy once 3d starts filling.
4. Remove both 4s electrons, then one more electron from the 3d subshell.
5. $$Fe^{3+}: [Ar] 3d^5$$

**Check your understanding**

Test your understanding of ion configurations:

1. What is the correct electron configuration of V²⁺ (vanadium(II), Z = 23 for V)?

   - [Ar] 3d³
   - [Ar] 4s² 3d¹
   - [Ar] 3d¹ 4s²
   - [Ar] 4s² 3d³

   *Why:* Correct! 4s electrons are always lost before 3d when transition metals form cations.

## Common Exceptions to Filling Rules

A small number of neutral atoms have unexpected electron configurations due to the extra stability of fully filled or half-filled d subshells. Symmetric electron distribution and low repulsion make these configurations lower energy than the expected Aufbau filling pattern.

**Worked example:** Explain why copper's electron configuration is not the expected $[Ar] 4s^2 3d^9$

1. Following generic Aufbau filling rules, the expected configuration for copper (Z = 29) is $[Ar] 4s^2 3d^9$.
2. A fully filled 3d subshell ($3d^{10}$) has extra stability from symmetric electron distribution and reduced electron-electron repulsion.
3. One electron is promoted from the 4s orbital to the 3d orbital to achieve this lower energy state.
4. $$\text{Actual ground state configuration: } [Ar] 4s^1 3d^{10}$$

> **Exam tip**
>
> Only chromium ($[Ar]4s^13d^5$) and copper ($[Ar]4s^13d^{10}$) are required to be memorized for IB HL exams.

## Common pitfalls

- **Wrong:** Writing 4s before 3d in the final electron configuration
  - Why it fails: Filling order is 4s before 3d, but exam markers require configurations ordered by principal quantum number $n$
  - Correct: Order subshells by increasing $n$, so 3d always comes before 4s in the final configuration
- **Wrong:** Removing 3d electrons before 4s when writing transition metal cation configurations
  - Why it fails: Once 3d starts filling, 4s electrons have higher energy and are lost first during ionization
  - Correct: Remove all $ns$ electrons first, then remove additional electrons from $(n-1)d$ as needed
- **Wrong:** Forgetting the exceptions for Cr and Cu, writing them as $4s^23d^4$ and $4s^23d^9$
  - Why it fails: Generic filling rules do not account for the extra stability of half-filled and fully filled d subshells
  - Correct: Memorize: Cr = $[Ar]4s^13d^5$, Cu = $[Ar]4s^13d^{10}$
- **Wrong:** Using atomic number (proton count) as electron count for charged ions
  - Why it fails: Cations have fewer electrons than protons, anions have more electrons than protons
  - Correct: Total electrons = atomic number minus positive charge, plus negative charge
- **Wrong:** Pairing electrons early in degenerate orbitals to follow filling order
  - Why it fails: This violates Hund's rule and increases electron-electron repulsion
  - Correct: Always fill each degenerate orbital with one parallel spin electron before pairing any

## Cheatsheet

| Rule/Concept | Summary |
| --- | --- |
| Filling order | Lower $n+l$ first; lower $n$ for equal $n+l$ |
| Final configuration order | Ordered by increasing principal quantum number $n$ |
| Transition metal cation electron loss | $ns$ electrons lost before $(n-1)d$ electrons |
| Common exceptions (4th period) | Cr: $[Ar]4s^13d^5$; Cu: $[Ar]4s^13d^{10}$ |
| Condensed configuration | Use nearest preceding noble gas core in square brackets |

## What's next

Electron configurations are the foundation for understanding all periodic trends, chemical bonding, and reactivity of elements. The arrangement of electrons directly determines an atom’s ionization energy, electronegativity, the number of bonds it can form, and its overall chemical behavior. Mastery of this sub-topic is required for nearly all subsequent topics in IB Chemistry, from explaining periodic trends to predicting molecular geometry and reaction behavior in organic chemistry. This knowledge also underpins the study of transition metal chemistry, explored later in the course.

- [The mole concept](https://www.owlsprep.com/study/ib-chemistry-hl-u1-the-mole-concept/)
- [Ideal gas behaviour](https://www.owlsprep.com/study/ib-chemistry-hl-u1-ideal-gas-behaviour/)
- [Kinetic molecular theory](https://www.owlsprep.com/study/ib-chemistry-hl-u1-kinetic-molecular-theory/)

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