Atomic orbitals

IB Chemistry SL· Structure 2.1: The nuclear atom· 40 min read

1. What is an Atomic Orbital?★★☆☆☆⏱ 10 min

📘 Definition

Atomic orbital

Labeled by $n$ , subshell, and orientation (e.g. 1s, 2pₓ)

A region of space around the nucleus where the probability of finding an electron is approximately 95% (the standard threshold for atomic models)

Example:

A 1s orbital is the lowest energy orbital, closest to the nucleus

Unlike the fixed circular orbits proposed by Bohr's early atomic model, orbitals do not describe exact electron paths. They only represent statistical regions where an electron is likely to be found, consistent with the Heisenberg uncertainty principle.

📐 Worked Example

Explain one key difference between the Bohr model and the quantum mechanical orbital model of the atom

1
The Bohr model assumes electrons follow fixed, predictable circular paths around the nucleus.
2
This contradicts the Heisenberg uncertainty principle, which states we cannot know both an electron's exact position and momentum at the same time.
3
The quantum mechanical model describes orbitals as probability regions where an electron is likely to be found, which aligns with experimental evidence and the uncertainty principle.

2. Shapes of s, p and d Orbitals★★★☆☆⏱ 15 min

Orbitals are grouped into subshells, each with a characteristic shape that determines how electrons interact during chemical bonding. IB SL requires you to recognize and describe the shapes of the three most common subshell types.

s-orbitals: Spherically symmetric around the nucleus. All s subshells contain 1 orbital, holding a maximum of 2 electrons.
p-orbitals: Dumbbell shaped, with three different orientations along the x, y, and z axes. A p subshell has 3 orbitals, holding 6 electrons total (2 per orbital).
d-orbitals: Mostly cloverleaf shaped, with five different orientations. A d subshell has 5 orbitals, holding 10 electrons total.

📘 Definition

Node

A region within an orbital where the probability of finding an electron is exactly zero. The number of nodes increases as the principal quantum number $n$ increases.

📐 Worked Example

Calculate the total number of orbitals and maximum electron capacity for the $n = 2$ shell

1
For $n = 2$ , there are two allowed subshells: $2 s$ and $2 p$ .
2
Count individual orbitals: $2 s$ has 1 orbital, $2 p$ has 3 orbitals, for $1 + 3 = 4$ total orbitals.
3
Each orbital holds a maximum of 2 electrons, so total capacity is $4 \times 2 = 8$ electrons.

Exam tip:

Always clarify if you are referring to a single orbital or a full subshell: this is the most common point of confusion in exam answers.

3. Quantum Numbers and Orbital Energy★★★☆☆⏱ 15 min

Each orbital is defined by a set of quantum numbers that determine its size, shape, orientation, and energy. IB SL requires you to understand the two most important quantum numbers that describe orbitals.

Quantum number	Allowed values	Property determined
$n$ (principal)	1, 2, 3...	Overall energy and size of the shell: higher $n$ = higher energy, larger orbital
$l$ (azimuthal)	0 to $n - 1$	Subshell type: $l = 0 = s$ , $l = 1 = p$ , $l = 2 = d$

Within an isolated atom, all orbitals in the same subshell have equal energy (they are called degenerate). Orbital energy increases with $n$ , and for the same $n$ , energy follows the order: $s < p < d$ .

📐 Worked Example

State the allowed subshells for $n = 3$

1
The azimuthal quantum number $l$ can only take integer values from 0 to $n - 1$ . For $n = 3$ , this means $l = 0, 1, 2$ .
2
Map $l$ values to subshell names: $l = 0$ is $s$ , $l = 1$ is $p$ , $l = 2$ is $d$ .
3
The allowed subshells for $n = 3$ are therefore $3 s$ , $3 p$ , and $3 d$ .

4. Common Pitfalls

Wrong move:

Describing orbitals as fixed circular electron orbits

Why:

This repeats the incorrect Bohr model, and exam markers will always penalize this wording

Correct move:

Describe orbitals as regions of space with a high (~95%) probability of finding an electron

Wrong move:

Claiming a p orbital holds 6 electrons

Why:

This confuses individual orbitals with full p subshells, which contain 3 separate orbitals

Correct move:

State that each individual orbital holds 2 electrons, so a full p subshell holds 6 total electrons

Wrong move:

Saying a 1p subshell is allowed

Why:

For $n = 1$ , the maximum value of $l$ is $n - 1 = 0$ , so only the 1s subshell can exist

Correct move:

Remember that $l$ can never be equal to or larger than $n$ , so 1p, 2d are impossible subshells

Wrong move:

Defining nodes as regions of low electron probability

Why:

Nodes have exactly zero probability, not just low probability, so this definition is incorrect

Correct move:

Define a node as a region where the probability of finding an electron is exactly zero

5. Quick Reference Cheatsheet

Subshell type	Number of orbitals	Max total electrons	Shape
s	1	2	Spherical
p	3	6	Dumbbell (3 orientations)
d	5	10	Cloverleaf (5 orientations)

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · 1
Identify shape of p orbital
2023 · 2
Compare properties of s and p orbitals

Going deeper

syllabusOfficial IB Chemistry SL SyllabusFull topic reference for Structure 2

What's Next

Understanding atomic orbitals is the foundation for writing electron configurations, which explains everything from the structure of the periodic table to the chemical reactivity of elements. Next, you will apply what you have learned about orbital energy levels to fill orbitals with electrons according to the Aufbau principle, Pauli exclusion principle, and Hund’s rule. This knowledge is also the starting point for understanding covalent bonding, periodic trends, and chemical reactivity, all core topics heavily assessed in IB Chemistry SL exams. Mastery of orbital shape and energy will help you predict bond angles, molecular shapes, and ionization energy trends later in the course.