C2.2 Write electron configurations using Pauli, Hund, and aufbau rules

Ontario Grade 12 Chemistry

Structure and Properties of Matter

Applying the Pauli, Hund, and aufbau rules

Atoms cannot be seen directly, but the way they interact with other substances depends in part on how their electrons are arranged. An electron configuration is a compact way to describe that arrangement. In this lesson, you will use three rules—aufbau, Pauli, and Hund—to write configurations. You will first review the meaning of atomic number and electron count, then practise with one complete example.

What you will learn

Explain how an electron configuration represents the arrangement of an atom’s electrons.
Use the aufbau rule to place electrons in the correct order of sublevels.
Apply the Pauli exclusion principle and Hund’s rule when showing electrons in orbitals.
Write and check an electron configuration for a neutral atom.

1. From atomic number to electron count

An atom contains protons, neutrons, and electrons. Protons have a positive charge, electrons have a negative charge, and neutrons have no charge. The atomic number tells you the number of protons in an atom. For a neutral atom, the number of electrons equals the number of protons.

A sublevel is a part of an atom’s electron arrangement that can hold a limited number of electrons. The sublevels used here are

s

,

p

, and

d

. An orbital is a region represented in a simple model as able to hold up to two electrons. An

s

sublevel contains one orbital, a

p

sublevel contains three, and a

d

sublevel contains five.

Electron configurations list sublevels and show how many electrons each contains. For example, the final superscript in

1s^2

means that the

1s

sublevel contains two electrons. The number before the letter identifies the main energy level. The letter identifies the sublevel. The superscript is an electron count, not a charge.

s^2,\ p^6,\ d^{10}

For a neutral atom, electron count equals atomic number.
An orbital holds at most two electrons.
The maximum capacities are $s^2$ , $p^6$ , and $d^{10}$ .

2. The three rules for placing electrons

The aufbau rule gives the order for filling sublevels. Aufbau means “building up”: place electrons in the available lower-energy sublevel before moving to the next one. For the elements considered in this lesson, use this order:

1s

,

2s

,

2p

,

3s

,

3p

,

4s

, then

3d

. Follow the order rather than filling every sublevel in one main energy level before moving on.

The Pauli exclusion principle says that an orbital can contain no more than two electrons. If two electrons occupy the same orbital, they must have opposite spins. In an orbital diagram, spin is shown with arrows pointing up and down. A paired orbital is written as

\uparrow\downarrow

.

Hund’s rule applies when a sublevel has several orbitals of the same energy, such as the three orbitals in a

p

sublevel. Put one electron in each orbital before pairing electrons. These single electrons are shown with arrows pointing the same way. After each orbital has one electron, additional electrons pair up. This rule helps you draw the orbital arrangement correctly; it does not change the total number of electrons in the sublevel.

The three rules work together. Aufbau determines which sublevel is filled next. Pauli limits how many electrons fit in each orbital. Hund determines how electrons occupy equal-energy orbitals within a sublevel.

1s\rightarrow2s\rightarrow2p\rightarrow3s\rightarrow3p\rightarrow4s\rightarrow3d

Fill sublevels in the stated order.
Put no more than two opposite-spin electrons in one orbital.
Fill equal-energy orbitals singly before pairing them.

3. Turning the rules into a configuration

To write a configuration, first find the number of electrons. For a neutral atom, use its atomic number. Next, follow the filling order and add electrons until the electron count is used. Respect the capacity of each sublevel. Check that the superscripts add to the atom’s total electron count.

When a question asks you to show orbitals as well as the configuration, draw separate boxes or spaces for orbitals in the same sublevel. Place one arrow in each orbital before adding pairs. For example, a

p^4

arrangement has four electrons in three orbitals: one orbital is paired, and each of the other two has one electron. The two unpaired arrows point in the same direction.

A written configuration does not show the arrow directions. It gives the number of electrons in each sublevel. The orbital diagram is a useful check on whether Pauli’s principle and Hund’s rule have been followed.

Count the electrons before filling sublevels.
Check both the order and the capacity of every sublevel.
For a final check, add all superscripts and compare the sum with the electron count.

4. Worked example: sulfur

Sulfur has atomic number

16

. The example asks for its electron configuration and an orbital check of its final occupied sublevel. Sulfur is neutral, so it has the same number of electrons as protons.

Begin with 16 electrons. Fill the sublevels in the stated order. The first two sublevels hold two electrons each. The

2p

sublevel can hold six, as can the

3p

sublevel. Continue until all 16 electrons have been placed.

The neutral sulfur atom has 16 electrons.
The final $3p$ sublevel contains four electrons.

Worked example

Sulfur’s electron configuration

Write the electron configuration for a neutral sulfur atom. Then show how its

3p

electrons occupy the three

p

orbitals.

Find the electron count
Sulfur’s atomic number is 16, so it has 16 protons. Because the atom is neutral, it also has 16 electrons.
$N_e=16$
Fill sublevels in order
Use the aufbau order and fill each sublevel up to its capacity before moving on. The counts are 2 in $1s$ , 2 in $2s$ , 6 in $2p$ , 2 in $3s$ , and 4 in $3p$ . The $3p$ sublevel is not full, so stop after placing the remaining electrons there.
$1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^4$
Check the $3p$ orbitals
A $p$ sublevel has three orbitals. Hund’s rule says to put one electron in each orbital before pairing. For four electrons, the first three occupy separate orbitals with parallel arrows; the fourth pairs in one orbital. The pair has opposite spins, as Pauli’s principle requires.
$3p: \uparrow\downarrow \uparrow \uparrow$
Verify the total
Add the superscripts. The total is 16, matching sulfur’s electron count. Each sublevel is within its capacity, and the final orbital arrangement follows Hund’s and Pauli’s rules.
$2+2+6+2+4=16$

Answer: Sulfur’s electron configuration is

1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^4

.

Check: The superscripts sum to 16, and the

3p

orbitals contain one pair and two single electrons.

Common mistakes and how to avoid them

Using the mass number to determine the electron count.

Correction: Use atomic number for the proton count. For a neutral atom, electron count equals proton count.

Putting three electrons into one orbital because a

p

sublevel holds six.

Correction: A

p

sublevel has three orbitals, and each orbital holds at most two electrons. Its total capacity is six.

Pairing electrons in one

p

orbital before placing one in each of the three orbitals.

Correction: Apply Hund’s rule: place one electron in each equal-energy orbital first, then begin pairing.

Giving paired electrons the same arrow direction.

Correction: Electrons sharing an orbital must have opposite spins, shown by one up arrow and one down arrow.

Stopping after filling

3p

when the next sublevel is needed.

Correction: Follow the complete filling order provided. In the sequence used here,

4s

comes before

3d

.

Lesson summary

For a neutral atom, the number of electrons equals its atomic number.
Use the aufbau order to decide which sublevel receives electrons next.
Use the Pauli exclusion principle to limit each orbital to two opposite-spin electrons.
Use Hund’s rule to fill equal-energy orbitals singly before pairing.
Add the configuration’s superscripts to check the total electron count.

Check your understanding

Question 1

A neutral atom has atomic number 13. How many electrons does it have?

13
12
14
26

Show answer and explanation

13

A neutral atom has equal numbers of protons and electrons. Atomic number 13 means 13 protons, so it has 13 electrons.

Question 2

Which statement correctly describes how to fill the three orbitals in a

p

sublevel?

Place up to three electrons in one orbital first.
Place one electron in each orbital before pairing.
Place pairs in two orbitals before using the third.
Place all electrons in separate orbitals, even after each has one.

Show answer and explanation

Place one electron in each orbital before pairing.

Hund’s rule says to place one electron in each equal-energy orbital before pairing. A

p

sublevel has three orbitals.

Question 3

What is the maximum number of electrons that can occupy one orbital?

1
2
3
6

Show answer and explanation

2

The Pauli exclusion principle limits an orbital to two electrons. If both are present, they have opposite spins.

Key terms

Atomic number: The number of protons in an atom’s nucleus.
Electron configuration: A notation that shows how an atom’s electrons are distributed among sublevels.
Sublevel: A part of an electron arrangement identified by a number and a letter such as $2p$ .
Orbital: A region in the model of an atom that can hold up to two electrons.
Aufbau rule: The rule that electrons fill available lower-energy sublevels before higher ones.
Pauli exclusion principle: The rule that an orbital holds at most two electrons, which must have opposite spins if paired.
Hund’s rule: The rule that electrons occupy equal-energy orbitals singly before pairing.

Continue through SCH4U

View the complete SCH4U Ontario Grade 12 Chemistry curriculum and lessons

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation C2.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

Official curriculum reference

Report a correction or ask a question

C2.2 · Write electron configurations using Pauli, Hund, and aufbau rules

Ontario Grade 12 Chemistry

Applying the Pauli, Hund, and aufbau rules

What you will learn

1. From atomic number to electron count

2. The three rules for placing electrons

3. Turning the rules into a configuration

4. Worked example: sulfur

Sulfur’s electron configuration

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SCH4U

About this lesson and its review