Angular Momentum Quantum Number: Definition & Example

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  • 3:41 Shapes of Orbitals
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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.

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