# Principal Quantum Number: Definition & Example

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• 0:25 What is the Principal…
• 1:11 Visualization
• 3:00 Subshells and Electrons
• 3:50 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.

Quantum numbers were developed to characterize electrons - its electron configuration, movement and position in an atom. Each electron has a unique set of quantum numbers. Of the four quantum numbers, our focus in this lesson is the principal quantum number.

## What is the Principal Quantum Number?

Let us imagine an apartment building with multiple floors - the more floors there are, the more people can reside in the building, and each person's address is different, based on the room and floor they occupy.

Just like each person or family occupies different floors in the apartment building, for electrons, they occupy different principal electron shells. How do we know which principal electron shell these electrons occupy? The principal quantum number tells us which principal electron shells the electrons occupy. For example, the electron configuration of helium (He), is 1s^2 - the principal quantum number is the number '1'. This means the two electrons of helium occupy the first principal electron shell.

Just like the apartment building, we have a first floor, second floor, third floor and so on. To assign the principal quantum numbers, we use the symbol n, where you can assign values to n, and these values are:

If you occupy a higher floor, and if there is no elevator, you need to spend more energy going to where you need to be. In the same way, as n increases, this means that the energy of the electron also increases.

## Visualization

When there are more floors in an apartment building that means more people can occupy the building and spread out more on each floor. If there are not as many floors, the people occupying the building are more concentrated in a smaller space. The same can be said about the principal quantum number and electron density.

The principal quantum number tells us not only the energy of an electron, but also gives us an idea about the electron density around the nucleus of an atom. In the illustration below, it shows on the left that when the principal quantum number is smaller the electron density is more concentrated closer to the atom, which means the electron cloud is smaller. On the right, the electron density is more spread out when the principal quantum number is larger, and the electron cloud is larger.

Based on the previous illustration, we can conclude that higher values of n have a larger atomic radius, and a greater distance between the nucleus and the electron. The attraction between electrons and the nucleus is not as strong for an atom with a larger atomic radius. This means that the energy needed to remove an electron, the ionization energy, is smaller when the atomic radius is larger due to the lower attraction between the nucleus and the electron.

The space in between each floor of an apartment building is a space that people cannot occupy. Electrons also have a space that they cannot occupy, called a node. A node is an area where there is zero probability of finding an electron. The principal quantum number also tells us about the number of nodes in an atom.

The total number of nodes is determined from the principal quantum number, n, subtracting one from n. So, the total number of nodes is equal to n - 1, as shown in the previous illustration. As the principal quantum number n increases, so does the electron density and the number of nodes.

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