Electron Configurations & the Four Quantum Numbers

Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

The nucleus of an atom is surrounded by a cloud of electrons. Discover how these electrons are structured around the nucleus by learning about electron configurations and the four quantum numbers.

Building Our Universe

What do you think is the most important building material? Is it wood, steel, bricks, concrete, or something else? If you ask me, it's something a lot more basic than any of those materials: atoms. Atoms are the building blocks of our universe. Everything you can see and touch is made of them.

Atoms are categorized into different types called elements. Each element is defined by the number of protons in that atom. We call this the atomic number, which can be seen on the periodic table.

Example of an Element on the Periodic Table
periodic table element

A neutral atom has the same number of electrons as it does protons. These electrons are what let atoms work as building blocks for everything in the universe. Neither you, I, nor any object or person you can think of in your everyday life would exist without electrons. Since electrons are so important, we'll delve deeper into learning how they are structured in an atom.

Electron Configuration

In order to see how the electrons are structured around an atom's nucleus we use something called an electron configuration. Let's dive straight in, and learn about electron configurations by looking at an example element.

magnesium electron configuration

In this electron configuration we have a bunch of letters and numbers raised to different powers. Each letter and number pair represents a group of electron orbitals in the atom. An orbital tells us the approximate positions in which electrons surround the nucleus. The numbers in superscript represent the number of electrons in each orbital group. The total number of electrons each group can have is determined by the letter; s can have 2 electrons, p can have 6, d can have 10, and f can have 14.

So, how do we go about filling out an electron configuration ourselves? The orbital groups are filled out in order according to Madelung's rule, which can best be visualized by a chart.

Electron Configuration Chart
Madelung rule

Let's try using this chart to fill out an example electron configuration for a selenium (Se) atom. Selenium has an atomic number of 34, and therefore has 34 electrons to fit into their proper orbital groups. To write out selenium's electron configuration you just follow the arrows starting at the top, and work your way down the electron configuration chart. Following these instructions we find that selenium has the following electron configuration.

selenium electron configuration

Four Quantum Numbers

We've seen how to write out electron configurations, but so far we've been glossing over what those numbers and letters in the configurations mean. We call these numbers and letters quantum numbers, and they tell us about different properties of electrons and their orbitals. There are a total of four quantum numbers. Let's go over each of them.

Principal Quantum Number

The first quantum number is the principal quantum number (n). This is the number we see in each number and letter orbital group pair in an electron configuration. The principal quantum number tells us two things. First, it tells us the electron's energy level, which we often refer to as its shell. Second, it tells us the orbital's size. Principal quantum numbers are represented as integers with a smallest possible value of 1.

n = 1, 2, 3, ...

Here n = 1 is the lowest energy level of an electron, also known as the ground state. Then n = 2, n = 3, and so on are excited states with higher energies. Also, as n increases so does the orbital's size.

Angular Momentum Quantum Number

The angular momentum quantum number (l) is the letter that follows the principal quantum number in an atom's electron configuration. We consider them sub-shells of the electron energy level shells. These letters represent the various shapes that the orbitals take.

Electron Orbital Shapes
orbital shapes

We can find an orbital's shape if we know the value for l, which always starts at a value of 0 and goes to a maximum of n - 1.

Let's look at the example of n = 3. This means l will consist of integers from 0 to n - 1.

n - 1 = 3 -1 = 2

l = 0, 1, 2

Every value of l corresponds to a different orbital shape. Here we have l = 0 which corresponds to the s orbital shape, l = 1 corresponds to the p orbital shape, and l = 2 the d orbital shape.

Magnetic Quantum Number

Our final two quantum numbers aren't represented visually in the electron configuration. The first of these two is the magnetic quantum number (ml). This tells the orientation of an orbital around the nucleus. The number of orbital orientations depends on the electron's angular momentum quantum number. Specifically, the values for ml are integers in the range -l to +l.

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