Back to: Inorganic Chemistry 100 Level
Welcome to class!
It’s always a pleasure to see you here, ready to learn. Let me begin with a picture you can relate to. Imagine you’re at the National Stadium in Abuja. If a football is kicked high into the air, sometimes you can guess where it is most likely to land by looking at its direction and speed. In the same way, when we talk about electrons in an atom, we can never say exactly where they are, but we can predict where they are most likely to be found. This idea is explained by radial probability distribution and angular probability distribution.
Radial And Angular Probability Distribution
The Idea of Probability in Orbitals
From quantum mechanics, electrons don’t move around the nucleus in fixed circular paths. Instead, they occupy orbitals, which are regions where they are most likely to be found. To describe this likelihood, scientists use probability distributions.
Radial Probability Distribution
The radial probability distribution tells us how likely it is to find an electron at a certain distance from the nucleus.
Think of throwing stones into a calm pond and watching the ripples spread outward. The distance from the centre shows how far electrons might be from the nucleus.
For example, in the hydrogen atom, the highest radial probability for the 1s electron is close to the nucleus. For 2s or 3s orbitals, electrons are more likely to be found farther away, though sometimes with smaller peaks closer in.
In simple words: the radial distribution describes “how far” the electron is from the nucleus.
Angular Probability Distribution
The angular probability distribution tells us the likelihood of finding an electron in a particular direction around the nucleus.
This distribution explains the shape of the orbitals. For example:
The s-orbital has the same probability in all directions (spherical).
The p-orbitals have higher probability in certain directions along the x, y, or z axis, giving them their dumbbell shape.
d and f orbitals have more complex angular distributions, which create their clover-like or multi-lobed shapes.
In simple words: the angular distribution describes “which direction” the electron is likely to be found.
Putting It Together
Radial distribution: “distance from the nucleus.”
Angular distribution: “direction from the nucleus.”
When combined, they give the complete picture of an orbital—its size and its shape.
Why Is This Important?
Understanding these distributions helps explain why orbitals look the way they do, why some orbitals penetrate closer to the nucleus (like s-orbitals), and why chemical bonding depends on orbital overlap in certain directions.
Summary
- Electrons are located in orbitals, not fixed paths.
- Radial probability distribution → likelihood of finding an electron at a certain distance from the nucleus.
- Angular probability distribution → likelihood of finding an electron in a certain direction (orbital shape).
- Together, they explain the size and shape of orbitals.
Evaluation
- What does radial probability distribution describe?
- Which orbital has equal angular probability in all directions?
- Why do p-orbitals have a dumbbell shape?
Excellent job today! You’re beginning to see electrons not as random specks but as beautiful, patterned clouds of probability. With Afrilearn, every step you take makes Chemistry simpler, clearer, and more exciting.