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Magnetic Quantum Number: Definition & Example Video

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  • 0:00 The Magnetic Quantum Number
  • 1:55 Relationship Among…
  • 4:10 Orientations
  • 5:25 Examples
  • 6:45 Lesson Summary
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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 are found within shells. These shells are further divided into subshells, which are further divided into orbitals. In this lesson, we will discuss the magnetic quantum number, which tells us about the orbitals an electron occupies.

The Magnetic Quantum Number

We have addresses to tell our friends where we live. In the world of subatomic particles, electrons also have an 'address' that gives us an idea where they are located in an atom. A specific set of quantum numbers helps us out in identifying where electrons are in an atom.

In this lesson, we'll discuss the magnetic quantum number - also known as the third quantum number - subshells, and orbitals, and their relationships to one another. The magnetic quantum number tells us about the orbital that an electron occupies - it determines how many orbitals there are as well as their orientation within a subshell. Its symbol looks like this:

Magnetic Quantum Number Symbol

In order to keep things clear going forward, let's review a few key terms. Orbitals are regions in space that are occupied by electrons. To visualize this better, take a look at this illustration:

Shells and Subshells

The electrons are found in shells surrounding the nucleus. The shell that an electron occupies is defined by the principal quantum number or the first quantum number. These shells are further divided into subshells. Subshells can be s, p, d or f. The subshells that an electron occupies are defined by the angular momentum quantum number or the secondary quantum number.

These subshells are further divided into orbitals. This helps us further narrow down the location of an electron. The four subshells (s, p, d, f) each have a specific number of orbitals. One orbital can be occupied by a maximum of two electrons. We can think about an orbital as a room with two twin beds: there is no bed for a third person, so the maximum occupancy for the room is two. This table summarizes all of the information we just covered:

Subshells and Orbitals

Now that we have been reacquainted with the first and second quantum numbers and the essential background information, we can now discuss the third quantum number, the magnetic quantum number.

Relationship Among Quantum Numbers

Since the magnetic quantum number is the third quantum number, it's important to know its relationship with the first two quantum numbers before we proceed further. Let's take a second to briefly review the first two quantum numbers.

The principal quantum number, n, tells us the principal shell is occupied by an electron, and can be any positive integer (n = 1, 2, 3, 4…). Its location is further narrowed down by the angular momentum quantum number, l, which tells us the subshell and its general shape. The value of l is dependent on the value of n (l = 0, 1, 2… n-1). The values of l correspond to specific subshells (l = 0 for s; l = 1 for p; l = 2 for d; l = 3 for f). These relationships are summarized in this table:

Principal and Angular Momentum Quantum Numbers

The magnetic quantum number further divides these subshells into orbitals and tells us about the orientation of these orbitals in space in relation to the other orbitals. Knowing about this tells us more about an electron and its location within an atom.

There are different possible values for the magnetic quantum number depending on the angular momentum quantum number. The number of orbitals can be determined from the angular momentum quantum number, l, and the possible values of ml can be determined from the following equations:

Magnetic Quantum Number Equations

To show the possible values of ml from l, let's take a look at this table:

Angular Momentum and Magnetic Quantum Numbers

According to the information provided by the table, for l = 0, there's only one possible orientation because there is only one value for ml. For l = 1, there are three possible orientations because there are three values of ml. For l = 2, there are five possible orientations because there are five values of ml. And for l = 3, there are seven possible orientations because there are seven values of ml.

Magnetic Quantum Number Orientations

Now that we've shown the relationship of the three quantum numbers with each other, we can talk about the different orientations associated with the values of the magnetic quantum number.

For the s subshell (l = 0), there is only one possible orientation of the orbital, since there is only one value of the magnetic quantum number, which is zero. The only orientation of s will look like this:

s orbital orientation

For the p subshell (l = 1), there are three possible orientations of the orbitals, since there are three values for the magnetic quantum number (-1, 0, +1). The three possible orientations will look like this:

d orbitals orientations

For the d subshell (l = 2), there are five possible orientations of the orbitals, since there are five values for the magnetic quantum number (-2, -1, 0, +1, +2). The five possible orientations will look like this:

d orbitals orientations

For the f subshell (l = 3), there are seven possible orientations of the orbitals, since there are seven values for the magnetic quantum number (-3, -2, -1, 0, +1, +2, +3). The seven possible orientations will look like this:

f orbitals orientations

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