# Atomic orbitals

> IB Chemistry SL · Structure 2: Electron Configuration
> Source: https://www.owlsprep.com/study/ib-chemistry-sl-u2-atomic-orbitals/

This module covers the quantum mechanical model of the atom, explaining the nature, shapes and energy levels of atomic orbitals, the core concept that underpins all electron configuration and bonding in IB Chemistry SL.

**Prerequisites:** [Basic atomic structure (protons, neutrons, electrons)](https://www.owlsprep.com/study/ib-chemistry-sl-u1-atomic-structure/)

## Learning objectives

- Distinguish between orbitals, shells, and subshells
- Describe the shapes of s, p, and d orbitals
- Interpret quantum numbers that define orbitals
- Relate orbital properties to energy level

## What is an Atomic Orbital?

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

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

*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.

> **warning**
>
> Exam markers routinely penalize descriptions that frame orbitals as fixed circular paths, so always use probability language.

**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.

## Shapes of s, p and d Orbitals

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.

**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: $2s$ and $2p$.
2. Count individual orbitals: $2s$ has 1 orbital, $2p$ 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.

## Quantum Numbers and Orbital Energy

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 $3s$, $3p$, and $3d$.

## Common pitfalls

- **Wrong:** Describing orbitals as fixed circular electron orbits
  - Why it fails: This repeats the incorrect Bohr model, and exam markers will always penalize this wording
  - Correct: Describe orbitals as regions of space with a high (~95%) probability of finding an electron
- **Wrong:** Claiming a p orbital holds 6 electrons
  - Why it fails: This confuses individual orbitals with full p subshells, which contain 3 separate orbitals
  - Correct: State that each individual orbital holds 2 electrons, so a full p subshell holds 6 total electrons
- **Wrong:** Saying a 1p subshell is allowed
  - Why it fails: For $n=1$, the maximum value of $l$ is $n-1=0$, so only the 1s subshell can exist
  - Correct: Remember that $l$ can never be equal to or larger than $n$, so 1p, 2d are impossible subshells
- **Wrong:** Defining nodes as regions of low electron probability
  - Why it fails: Nodes have exactly zero probability, not just low probability, so this definition is incorrect
  - Correct: Define a node as a region where the probability of finding an electron is exactly zero

## 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) |

## 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.

- [Electron Configuration Rules](https://www.owlsprep.com/study/ib-chemistry-sl-u2-electron-configuration-rules/)
- [Atomic emission spectra](https://www.owlsprep.com/study/ib-chemistry-sl-u2-atomic-emission-spectra/)
- [First ionization energy trends](https://www.owlsprep.com/study/ib-chemistry-sl-u2-first-ionization-energy-trends/)

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