Angular Momentum Quantum Number: Definition & Example

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Archimedes' Principle: Definition, Formula & Examples

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:01 Angular Momentum…
  • 1:28 Relationship with…
  • 3:41 Shapes of Orbitals
  • 4:05 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Login or Sign up


Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Nissa Garcia

Nissa has a masters degree in chemistry and has taught high school science and college level chemistry.

Electrons in an atom occupy regions known as orbitals, and these orbitals have shapes. In this lesson, we will discuss the secondary quantum number: the angular momentum quantum number, which determines the shape of an orbital.

Angular Momentum Quantum Number

There are four quantum numbers that make up the address for an electron. Of the four quantum numbers, our focus for this lesson is the angular momentum quantum number, which is also known as the secondary quantum number or azimuthal quantum number.

The angular momentum quantum number is a quantum number that describes the 'shape' of an orbital and tells us which subshells are present in the principal shell. We can think about it this way: each of our homes has its own architecture. In the subatomic level, the 'home' of electrons is an orbital, and each orbital has its own shape. The symbol that is used when we refer to the angular momentum quantum number looks like this:

Symbol for Angular Momentum Quantum Number

Electrons occupy a region called 'shells' in an atom. The angular momentum quantum number, l, divides the shells into subshells, which are further divided into orbitals. Each value of l corresponds to a particular subshell. The lowest possible value for l is 0. This following table shows which subshells correspond to the angular momentum quantum number:

Subshells and Angular Momentum Quantum Number

The angular momentum quantum number can also tell us how many nodes there are in an orbital. A node is an area in an orbital where there is 0 probability of finding electrons. The value of l is equal to the number of nodes. For example, for an orbital with an angular momentum of l = 3, there are 3 nodes.

Relationship with Principal Quantum Number

It is important to point out that there is a relationship between the principal quantum number and the angular momentum quantum number. To recap, the principal quantum number tells us what principal shells the electrons occupy. It determines the energy level and size of the shell and uses the symbol n and is any positive integer.

The angular momentum quantum number values range from 0 to n - 1, and cannot be greater than n. This table shows the relationship between the two quantum numbers:

Relationship Between the Principal and Angular Momentum Quantum Numbers

We can think about the relationship between these two quantum numbers as this: the principal quantum number is the number of the floors, and the angular momentum quantum numbers are the rooms in each floor. The floor contains the rooms, and each room has its own unique appearance.

It's important to note that the value of l never exceeds n, and its greatest value is equal to n - 1. Let's go over a few examples to further understand this relationship.

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account