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Four Quantum Numbers: Principal, Angular Momentum, Magnetic & Spin

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  • 1:05 Electron Configurations
  • 2:07 Orbitals
  • 2:36 Principal Quantum Number
  • 4:08 Angular Momentum…
  • 5:37 Magnetic Quantum Number
  • 7:18 Spin Quantum Number
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Lesson Transcript
Instructor: Kristin Born

Kristin has an M.S. in Chemistry and has taught many at many levels, including introductory and AP Chemistry.

Each atom inside of an electron has its own 'address' that consists of four quantum numbers that communicate a great deal of information about that electron. In this lesson we will be defining each quantum number and explaining how to write a set of quantum numbers for a specific electron.

Four Quantum Numbers

The periodic table can be used to determine electron configurations.
Periodic Table Electron Configurations

How would you describe to someone exactly where you lived? I'm guessing you would start with your address. When you specify the location of a building, you usually list which country it's in, which city and state it's in in that country, and its street address. Just like no two buildings have the exact same address, no two electrons can have the same set of quantum numbers. Also, there are very specific rules about quantum numbers that can exist together, just like you wouldn't say that Wisconsin is a state in the country of Spain. A quantum number describes a specific aspect of an electron. Just like we have four ways of defining the location of a building (country, state, city, and street address), we have four ways of defining the properties of an electron, or four quantum numbers.

Electron Configurations

Before starting this lesson, you should have an understanding of what an electron configuration is and how to write one for an element. Remember that an electron configuration tells us where each electron is in an atom, and knowing the arrangement of the electrons is necessary in order to understand how an element will react and what types of molecules it will form. So let's start with an atom of silicon. What would its electron configuration be? You should have an answer of 1s2 2s2 2p6 3s2 3p2. Silicon has a total of 14 electrons, which are all represented by that electron configuration. So what do all those numbers and letters mean? This lesson is going to crack that electron configuration code.

The electron configuration for silicon
Silicon Electron Configuration

Orbitals

Before we go into great detail about those quantum numbers, it is important to note that when I say location, I mean probable location. There is really no way to know exactly where an electron is at a given time; they are very elusive. But it is possible to determine which specific three-dimensional region it is probably in. These three-dimensional boundaries where an electron is most likely found are called an atomic orbital.

Principal Quantum Number

The first quantum number that describes an electron is called the principal quantum number. It is often symbolized by the letter n. This number tells us the energy level or size of an orbital. The higher the number, the larger the region is. So let's take the electron configuration for silicon and look at the very last electron that was added to silicon. It should be one in the 3p orbital. That 3 indicates the principal quantum number. So for this electron, n = 3. The orbital that the last electron is going to be in will be larger than the 2p orbital because it has a higher number. This means that the 2p electron is more likely to be found closer to the nucleus than the 3p electron. You will also hear the term 'energy level' a lot when dealing with electrons and their locations. The 2p electrons are located in the second energy level and the 3p electrons are located in the third energy level. They will have more energy than the electrons in the 2p orbitals. So, in silicon, how many electrons will have n = 3 as one of their quantum numbers? The answer is 4. There are two 3s electrons and two 3p electrons. All start with 3, so all will have a principal quantum number of 3.

Angular Momentum Quantum Number

The angular momentum quantum number refers to the shapes of orbitals.
Angular Momentum Quantum Number Shapes

The next quantum number relates to the letters in the electron configuration. Which letters did you encounter when you wrote out electron configurations? You should have encountered s, p, d, and f. The letters represent the angular momentum quantum number. It sounds like a mouthful, but it's really just the shape of the orbital and is sometimes symbolized by the letter l. The s orbitals have a spherical shape, p orbitals are sort of dumbbell-shaped, d orbitals look similar to a three-dimensional four-leaf clover, and f orbitals have more of a flower shape. When assigning a number to each shape, the s-shaped orbitals have an l = 0, the p orbitals have an l = 1, the d orbitals have l = 2, and the f orbitals have l = 3. So that last electron that we added to the silicon atom in the 3p orbital will have an l = 1 and be sort of dumbbell-shaped. So for this electron the n = 3 and the l = 1. You may notice that some combinations of quantum numbers are going to be impossible. For example, you can't have n = 1 and l = 2 for a cluster of quantum numbers because that would mean that the electron configuration would have to be 1d, and there are no 1d electrons.

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