Worked example 1
How many unpaired electrons are in a ground-state Mn²⁺ ion (Mn, Z = 25)?
Try it first: Decide which electrons manganese loses before you count anything.
0 of 3 steps revealed.
Orbital diagramsCourse level: High School / HonorsCourse level: AP Chemistry
Orbital Diagrams, Hund's Rule and Magnetism
What you'll be able to do: Draw a correct orbital diagram and use it to count unpaired electrons and predict magnetic behaviour.
Best after: Electron Configurations and Orbital Filling
Introduction
A configuration such as 2p⁴ tells you how many electrons are in a subshell, but not how they are arranged inside it. Two short rules settle the arrangement, and the arrangement is what determines whether a substance is attracted to a magnet.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Apply the Pauli exclusion principle to a single orbital
- Apply Hund's rule to degenerate p and d orbitals
- Count unpaired electrons from a configuration
- Classify a species as paramagnetic or diamagnetic
One orbital, two electrons, opposite spins
The Pauli exclusion principle says no two electrons in an atom can share all four quantum numbers. Practically: an orbital holds at most two electrons, and if it holds two they must have opposite spins, drawn as one up arrow and one down arrow in the same box.
A box represents one orbital and an arrow represents one electron, with its direction indicating spin. In the usual diagram, p has three boxes and d has five. Pauli constrains each box separately: [↑↓] is allowed, [↑↑] is forbidden, and three arrows in any one box are forbidden. The arrows are spin labels, not literal directions in which electrons orbit the nucleus.
Hund's rule: spread out before pairing
Orbitals in the same subshell have equal energy. Electrons occupy them singly, all with the same spin, before any orbital gets a second electron. Nitrogen (2p³) therefore has three separate single electrons, not one pair plus one single.
Hund's rule applies within a set of equal-energy orbitals. It does not let you put an electron into 3p before filling lower-energy 3s merely to avoid a pair. For p² the ground-state pattern is [↑] [↑] [ ]; pairing both in one box satisfies Pauli but is a higher-energy arrangement. Thus an allowed occupancy can still fail to represent the ground state. Choosing all down arrows instead of all up arrows for the first singly occupied boxes is equally valid if the spins are parallel.
N 2p: up | up | up
Counting unpaired electrons
Write the configuration, fill the boxes of the last partly filled subshell using Hund's rule, and count the boxes holding just one arrow. For Fe³⁺ ([Ar] 3d⁵) all five d orbitals hold one electron, giving 5 unpaired electrons, the maximum possible for a d subshell.
Only the partly filled subshell can contribute unpaired electrons. Everything else is already paired.
Paramagnetic or diamagnetic
A species with at least one unpaired electron is paramagnetic and is drawn into a magnetic field. A species with every electron paired is diamagnetic and is weakly pushed out. Zn²⁺ ([Ar] 3d¹⁰) is diamagnetic, while Cu²⁺ ([Ar] 3d⁹) is paramagnetic with one unpaired electron.
Diamagnetic does not mean no electrons in the d subshell. It means no unpaired ones.
Draw the boxes before predicting magnetism
A p subshell contains three equal-energy orbitals, and a d subshell contains five. For an oxygen atom, 2p⁴ must distribute as [↑↓] [↑] [↑] (the identity of the paired box is arbitrary). Two electrons remain unpaired, so an isolated ground-state O atom is paramagnetic.
Merely seeing an even electron count does not imply all electrons are paired. In an orbital diagram, fill each box singly with parallel spins first, then add the opposite-spin partners; never put two same-spin arrows in one box.
The magnetic behavior of a complex or solid can require extra information about bonding, so the simple count here applies to the stated atomic or free-ion configuration.
Read unpaired-electron counts across a subshell
| Electrons in a p subshell | Ground-state unpaired electrons |
|---|---|
| p¹ | 1 |
| p² | 2 |
| p³ | 3 |
| p⁴ | 2 |
| p⁵ | 1 |
| p⁶ | 0 |
For five degenerate d orbitals, the corresponding sequence for d¹ through d¹⁰ is 1, 2, 3, 4, 5, 4, 3, 2, 1, 0. The count rises until every box is singly occupied, then falls as pairing proceeds. A filled core contributes no unpaired electrons, so [Ar] 3d⁷ has three unpaired electrons in the free-ion model.
An even total electron count is not sufficient to establish diamagnetism: p² has two unpaired electrons. Likewise, the behavior of an isolated O atom cannot simply be transferred to O₂ or a bulk solid. Bonding can create a different set of orbitals, and ligands can split d orbital energies in complexes. Use the species and model actually specified.
For p², draw two single arrows in different boxes, not a pair in one box.
Key ideas
Rule
Pauli exclusion principle
Two electrons in the same orbital must have opposite spins, so an orbital holds a maximum of two.
Rule
Hund's rule
Within a set of equal-energy orbitals, electrons occupy separate orbitals with parallel spins before pairing up.
Definition
Paramagnetic
Has one or more unpaired electrons and is attracted into a magnetic field.
Definition
Diamagnetic
Has all electrons paired and is very weakly repelled by a magnetic field.
Worked examples
Worked example 2
Is Zn²⁺ paramagnetic or diamagnetic?
0 of 3 steps revealed.
Worked example 3
For a ground-state oxygen atom (Z = 8), draw the 2p occupancy and predict its number of unpaired electrons.
Try it first: After [He] 2s², place four electrons in three p boxes.
0 of 3 steps revealed.
Worked example 4
Draw the 2p part of carbon's orbital diagram and predict its magnetic behavior.
Try it first: Carbon is 1s² 2s² 2p²; distribute only the 2p electrons.
0 of 3 steps revealed.
Common mistakes
| Mistake | Why it's wrong | Check instead |
|---|---|---|
| Pairing electrons in the first p orbital before using the others. | Degenerate orbitals are equal in energy, and pairing costs repulsion energy, so electrons spread out first. | Place one electron in every box of the subshell before adding a second to any box. |
| Assuming a full d subshell means paramagnetic because d electrons are present. | Magnetism depends on unpaired electrons, not on whether a subshell is occupied. | Count arrows that are alone in a box. Zero alone means diamagnetic. |
| Removing d electrons first when forming a transition-metal cation. | Once the atom has d electrons, the ns orbital is higher in energy, so ns electrons leave first. | For Fe²⁺ start from [Ar] 4s² 3d⁶ and remove the 4s pair to get [Ar] 3d⁶. |
Scroll horizontally if needed to read all columns.
After the lesson · Question bank
Independent practice
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What you should now know
The Pauli exclusion principle limits an orbital to two electrons with opposite spins, and Hund's rule spreads electrons singly across degenerate orbitals first. Counting the leftover unpaired electrons tells you whether a species is paramagnetic or diamagnetic.
- An orbital holds two electrons with opposite spins
- Electrons half-fill degenerate orbitals before pairing
- Unpaired electrons decide paramagnetic versus diamagnetic
- Transition metals lose ns electrons before (n-1)d electrons
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Sources and further reading
- Chemistry 2e, Section 6.4: Electronic Structure of Atoms (Electron Configurations)Flowers, Theopold, Langley, Robinson · OpenStax, Rice University · Chapter 6.4View source
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Source rights and review status - General Chemistry bookshelf (LibreTexts)LibreTexts, University of California, DavisView source
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