**2021-09-23**| Atomic Structure is more complicated than the simple electron shell model leads us to believe! And we can use Quantum Numbers to easily and concisely understand what a real atom looks like.

Hi everyone, in this video we'll be looking at how electrons are arranged in atoms, and how quantum numbers can be used to know more about each electron.

Quantum numbers are simple numbers that we can assign to every electron in an atom, and are related to quantities we are allowed to know at the same time as the Energy of each electron. If you've heard of Heisenberg's Uncertainty Principle, you'll know that in quantum mechanics we are not allowed to know certain quantities at the same time - an example being the position and momentum of a particle. Well the quantities relating to our quantum numbers are ones that we ARE allowed to know at the same time as the energy of the electron. (If you want to know more about Heisenberg's Uncertainty Principle, check out my video on this topic here: https://www.youtube.com/watch?v=iZ96TuP_veY&t=1s)

The first of these quantum numbers is known as the principal quantum number, and is usually given the label "n". The principal quantum number just tells us the energy level in which an electron can be found. You may have heard that electrons can only be found in specific energy levels within an atom. The energy level nearest to the nucleus (and therefore lowest in energy) is labelled n = 1. The next one is n = 2, and then n = 3, and so on as we get further away from the nucleus.

Just from finding out the principal quantum number of an electron, we find out something about how far it is (likely to be) from the nucleus, as well as the energy of the particle. So a lot of information is condensed down into one simple number, n = ?

The next quantum number is the azimuthal quantum number, or orbital angular momentum quantum number. To understand this, we need to first recall that within each shell, there are also "subshells". Every shell, given by the principal quantum number, can have subshells in it equal to the principal quantum number. In other words, n = 1 only has 1 subshell. n = 2 has 2 subshells, and so on.

In a particular subshell, an electron has a certain amount of angular momentum. An object has angular momentum if it is spinning or moving around a curved path (at least in classical physics). And here we are not talking about spin - an electron has spin regardless of where it is, in a subshell, or even in an atom. But the orbital angular momentum being discussed here, depends on which subshell the electron in question is found in.

In the n = 1 level, there is 1 subshell that looks spherical in terms of the wave function. This means the electron in this subshell can be found anywhere around the nucleus, with the most likely distance being given by the basic energy level diagram. In this subshell, the electron has 0 angular momentum. In other words, its azimuthal quantum number is l = 0.

In the n = 2 level, there are 2 subshells. The first is another spherical, l = 0 subshell. This sphere is bigger than the n = 1 sphere meaning the electron in this subshell is more likely to be found further away from the nucleus than the one in n = 1. However, the n = 2 shell also has a triple-dumbbell subshell. This means electrons are no longer equally likely to be found in any direction around the nucleus. The dumbbells in this subshell lie along the x, y, and z directions. And in this subshell, each electron has 1 x hbar units of angular momentum. Hbar is simply the Reduced Planck Constant. Due to this angular momentum, we give these electrons the quantum number l = 1.

Those are the quantum numbers discussed here. There are 2 more that allow us to uniquely define each electron in an atom, because no two electrons can have the exact same values for all 4 electrons. This is due to Pauli's Exclusion Principle, a topic I've covered in this video: https://www.youtube.com/watch?v=INYZy6_HaQE

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Timestamps:

0:00 - Using Quantum Numbers to Understand Atomic Structure

1:45 - Principal Quantum Number (n) to Represent Electron Shells

2:53 - Azimuthal Quantum Number (l) to Represent Subshells

6:25 - The Difference Between Subshells (Orbital Angular Momentum)

8:57 - The Remaining Quantum Numbers, and the Exclusion Principle