Parth G | How the Spin of an Electron Affects the Atom It's In - Spin-Orbit Coupling (Fine Structure): Parth G @ParthGChannel | Uploaded 3 years ago | Updated 2 hours ago
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Due to Spin-Orbit Coupling, we can see one way in which Spin actually affects the world around us. #Spin #SpinOrbitCoupling #AngularMomentum #QuantumPhysics

Hey everyone, in this video I wanted to discuss a real-world impact of spin. We've often heard about this rather mysterious property, where particles behave as if they have some sort of angular momentum even though they are not moving along any curved paths. But what effect does it have on the universe?

To begin, we'll recall that an electron has spin (a fixed amount of angular momentum) regardless of where it's found. But when found in a shell around a nucleus, it also has some amount of "orbital" angular momentum.

When charged particles such as electrons have angular momentum, they essentially behave as little magnets. They have a "magnetic dipole moment". This magnetic dipole moment will interact with any external magnetic field present in the same region of space as the particle. Interestingly from the perspective of an electron in an atom, there does indeed exist a magnetic field. This despite there not being one in the frame of reference of the nucleus, which only sees electric fields. The reason this can happen is because electric and magnetic fields look different from different reference frames, as discussed in special relativity. More on this here: https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity

The interaction between the magnetic field and the dipole moment of the electron, and therefore the energy change this causes to the electron, is proportional to the dot product (scalar product) between the external magnetic field and the dipole moment. This interaction term can actually be rewritten as the dot product between the orbital angular momentum and the spin angular momentum of the particle. This is what we refer to as spin-orbit coupling.

Now it turns out that within each electron shell, there are subshells. And each of these subshells have a different orbital angular momentum value. Therefore the energy of each subshell within a shell is very slightly different to all the other subshells, based on the spin-orbit coupling term.

In order to see these energy differences we have to look closely at the "fine structure" of the atom, but it does exist. The simplistic picture of each shell representing one energy level is not quite true. And this is a direct result of the fact that electrons have spin!

Check out this playlist if you want to watch some of my older videos covering topics that have only been skimmed over in this video: https://www.youtube.com/playlist?list=PLOlz9q28K2e5gAs7Ep9zD4EJ-4oTGg_2U

Timestamps:
0:00 - What effect does spin have in a real world context?
1:07 - Basic atomic structure and angular momentum (orbital and spin)
2:47 - Thanks to Skillshare for sponsoring this video - free trial of Premium in the description
3:47 - Charged particles and angular momentum: magnetic dipole moment
4:51 - Electromagnetic fields from different reference frames - special relativity!
5:42 - The interaction between magnetic dipole moment and external magnetic field
6:07 - Scalar products (dot products) visualized
6:39 - Spin-orbit coupling
7:35 - Electron subshells with different orbital angular momentum values
8:26 - Fine-structure splitting of electron shells
9:41 - Thanks for watching! New merch announcement

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How the Spin of an Electron Affects the Atom It's In - Spin-Orbit Coupling (Fine Structure): Parth G @ParthGChannel