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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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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.

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:

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:

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.

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:

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.

- Example 1: What orbital has a value of
*n*= 1 and*l*= 0? The answer is**1s**orbital. The number 1 is from the value of*n*and the letter 's' corresponds to*l*= 0. - Example 2: What orbital has a value of
*n*= 3 and*l*= 2? The answer is**3d**orbital. The number 3 is from the value of*n*and the letter 'd' corresponds to*l*= 2. - Example 3: Is it possible to have a set of quantum numbers with
*n*= 4 and*l*= 4? The answer is no, because the highest value for*l*is*n*- 1. In this case, the highest possible value for*l*is 3 and not 4. - Example 4: Is it possible to have a set of quantum numbers of
*n*= 4 and*l*= 2? The answer is yes, because*l*can go as high as*l*= 3. Since*l*= 2, this is still possible. - Example 5: What are the possible values of
*l*for*n*= 5? The answer is*l*= 0, 1, 2, 3, 4.

According to the definition of the angular momentum quantum number, it describes the shape of the orbital. As mentioned earlier, shells are divided into subshells (s, p, d and f). These subshells are divided into orbitals - the space which an electron occupies. There is a general shape for the orbitals for each subshell. These shapes are clearly outlined in this table:

The **angular momentum quantum number**, *l*, (also referred to as the secondary quantum number or azimuthal quantum number) describes the shape of the orbital that an electron occupies. The lowest possible value of *l* is 0, and its highest possible value, depending on the principal quantum number, is *n - 1*. The value of *l* also tells us the number of nodes; the number corresponding to *l* is the same as the number of nodes.

For the values of *l*, 0 corresponds to the s subshell, 1 corresponds to the p subshell, 2 corresponds to d, and 3 corresponds to f. Each subshell is divided into orbitals, and these orbitals have their own unique shape, depending on the value of the angular momentum quantum number.

**Angular momentum quantum number** - a quantum number that describes the 'shape' of an orbital and tells us which subshells are present in the principal shell

**Secondary quantum number** - another term for azimuthal quantum number

**Azimuthal quantum number** - see angular momentum quantum number

**Node** - an area in an orbital where there is 0 probability of finding electrons

**Principal quantum number** - number which determines what principal shells the electrons of an atom occupy

Upon completion of your in-depth exploration of the lesson, ensure that you can:

- Describe what the principal and angular momentum quantum numbers of an electron divulge about its location
- Discuss the relationship between the principal quantum number and the angular momentum quantum number
- Recognize the shapes of orbitals

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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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