Spin Quantum Number: Definition & Example

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  • 0:01 Spin Quantum Number
  • 1:18 Paramagnetism & Diamagnetism
  • 2:28 Determining the Spin…
  • 3:40 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.

There are four quantum numbers that describe the configuration of an electron. In this lesson, we will discuss the fourth quantum number, which is called the spin quantum number. This describes an electron's orientation within an atom.

Spin Quantum Number

Let's think about an electron in an atom; first, imagine a spinning top. A top can spin clockwise or counter-clockwise. In the same way, an electron occupying an orbital behaves like a spinning top.

The spin quantum number, also known as the fourth quantum number, is a number value that describes the orientation of an electron occupying an orbital. The symbol that we will use for the spin quantum number is ms.

Spin Quantum Number Symbol

Let's visualize the spin quantum number. The value of ms=+1/2 is shown by an arrow pointing upwards and is also said to be spin up. The value of ms=-1/2 is shown by an arrow pointing downwards and is also said to be spin down.

Spin Quantum Number Values

How do electrons enter orbitals? This is important when determining the sign of ms. Electrons singly occupy orbitals first and then they pair up, as shown in the following illustration. Each box represents one orbital, and an orbital can only have a maximum number of two electrons. There are three 'p' orbitals, and on the left side, it is shown how the 'p' orbitals are filled. There are five 'd' orbitals, and on the right side, it is shown how 'd' orbitals are filled as the number of electrons increases.

Occupying Orbitals

As we can see, in one orbital, the orientation of the two electrons is always the opposite of each other. One electron will be spin up, and the other electron is spin down. If the last electron that enters is spin up, then ms = +1/2. If the last electron that enters is spin down, then the ms = -1/2.

Paramagnetism and Diamagnetism

The spin of an electron makes it behave like a small magnet, in that the spin determines the magnetic property of an atom. Electrons are very small particles and their movement is limited. However, this movement still creates a small magnetic field.

For example, in an atom, all the electrons are paired in the orbitals. The spins, since they have values with opposite signs (+1/2 and -1/2), cancel each other out. We can therefore say that the atom is diamagnetic. Diamagnetic atoms have all of their electrons paired, and in each orbital, if you add their spins, the total will be zero, and they repel magnetic fields.


Now let's look at an atom that contains unpaired electrons in their orbitals. These unpaired electrons are alone in their orbitals. We can say therefore that these atoms with unpaired electrons are paramagnetic. Paramagnetic atoms have unpaired electrons, and they are attracted to a magnetic field. The electron in the orbital has a net spin, so the spins do not cancel each other out. In effect, the whole atom will have a net spin.


Determining the Spin Quantum Number

Let's go over the following examples so that we can determine the value of the spin quantum number based on the information given in the question:

  • Example 1: What is the correct value for ms for the last electron that enters the orbitals below? Is this atom paramagnetic or diamagnetic?

Example 1

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