Worked example 1
Write the ground-state electron configuration of a sulfur atom (Z = 16) and state how many unpaired electrons it has.
Try it first: Fill subshells in n + l order and stop at 16 electrons.
0 of 4 steps revealed.
BondingElectron orbitalsContent level: Core 18 min
Filling Orbitals: Aufbau, Pauli and Hund
What you'll be able to do: Apply the Aufbau, Pauli and Hund rules to build orbital diagrams and to work out ion configurations.
Best after: Orbitals, Subshells and Quantum Numbers
Introduction
Three short rules decide the order electrons fill orbitals, and they explain magnetism and ion charges alike.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Order subshells by energy using the n + l rule
- Write ground-state orbital diagrams for main-group atoms
- Apply the Pauli exclusion principle to reject impossible quantum number sets
- Use Hund rule to predict unpaired electrons and magnetic behaviour
- Write electron configurations for transition metal cations
Lesson
Aufbau and the n + l rule
Electrons occupy the lowest-energy subshell available. Order the subshells by n + l, and break ties by choosing the smaller n. That is why 4s (4 + 0 = 4) fills before 3d (3 + 2 = 5), and why 4p (5) fills after 3d even though both come before 5s (5, but with larger n).
Reading the periodic table left to right by blocks reproduces the same order without memorizing a diagram.
Pauli exclusion and Hund rule
The Pauli exclusion principle says no two electrons in an atom can share all four quantum numbers, which caps every orbital at two electrons with opposite spins. Hund rule says that within a set of degenerate orbitals, electrons spread out singly with parallel spins before any orbital takes a second electron, because pairing costs repulsion energy. Nitrogen therefore has three unpaired 2p electrons, not one pair and one single.
Ions and magnetism
When a transition metal ionizes, electrons leave the highest n first, so the 4s electrons go before the 3d electrons. Vanadium [Ar] 4s² 3d³ becomes V³⁺ with configuration [Ar] 3d². A species with any unpaired electrons is paramagnetic and is attracted to a magnetic field; a species with all electrons paired is diamagnetic.
Do not remove 3d electrons first for a cation, even though 3d was written after 4s.
Distinguish a forbidden diagram from an excited one
Pauli exclusion forbids two electrons in one orbital with the same spin. Hund's rule instead describes the lowest-energy way to distribute electrons among degenerate orbitals: occupy them singly with parallel spins before pairing. Violating Hund can give an excited arrangement, whereas violating Pauli makes a proposed orbital occupancy impossible.
Pauli decides what is allowed; Hund chooses the ground-state pattern.
Key ideas
Rule
Aufbau principle
Fill the lowest-energy subshell first, ordered by n + l with ties broken by smaller n.
Rule
Pauli exclusion principle
Two electrons in the same orbital must have opposite spins.
Rule
Hund rule
Half-fill degenerate orbitals with parallel spins before pairing.
Key concept
Fe²⁺
Iron is [Ar] 4s² 3d⁶, so Fe²⁺ is [Ar] 3d⁶ with four unpaired electrons and is paramagnetic.
Equation
Energy ordering
lower n + l fills first
Equation
Unpaired electron count
unpaired = number of singly occupied orbitals
Worked examples
Worked example 2
What is the electron configuration of Fe³⁺ (Z = 26)?
Try it first: Write neutral iron first, then decide which electrons leave.
0 of 3 steps revealed.
Worked example 3
Compare two proposed 2p² diagrams: A is [↑↑] [ ] [ ]; B is [↑↓] [ ] [ ]. Which is allowed, and which is the ground state?
Try it first: Inspect the arrows inside each box, then spread electrons across boxes.
0 of 3 steps revealed.
Common mistakes
Pairing electrons in one p orbital before filling the other two.
Why it's wrong: Pairing raises energy through electron repulsion, so Hund rule forbids it in the ground state.
Check instead: Place one electron in each degenerate orbital before doubling up.
Removing 3d electrons before 4s electrons when forming a cation.
Why it's wrong: Once 3d is occupied it drops below 4s in energy, so 4s electrons are the outermost.
Check instead: Take electrons from the highest principal quantum number first.
Assuming every ion with d electrons is paramagnetic.
Why it's wrong: A d¹⁰ ion such as Zn²⁺ has every electron paired.
Check instead: Draw the orbital diagram and count singly occupied orbitals.
After the lesson · Question bank
Independent practice
Work through new problems on this topic on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
No questions are available for this topic yet. Explore the unit question bank.
Your next step
Lesson: Not marked completed
Marking a lesson completed records that you finished reading it. Practice establishes mastery separately. Saved on this device.
Continue through the unit’s lessons and available practice.
What you should now know
Electrons fill the lowest available energy subshell first (Aufbau, ordered by the n + l rule), no two electrons share all four quantum numbers (Pauli), and degenerate orbitals each take one electron with parallel spin before pairing (Hund). Transition metals lose their outer s electrons before their d electrons when they ionize.
- Fill subshells by increasing n + l, breaking ties with the smaller n
- No orbital holds more than two electrons, and they must be opposite in spin
- Degenerate orbitals fill singly before any pairing occurs
- Cations lose electrons from the highest n first, so 4s empties before 3d
- Unpaired electrons mean paramagnetic, all paired means diamagnetic
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.