What is, really, the spin of an electron?

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(sorry for my english)

Hi everyone,

Earlier today, i was studying the electronic distribution of atoms and it was all going fine until it got to the part about spin. My textbook presented spin as if it was just a fact, with no causes or consequences, which is weird, since my physics teacher always tells us to try to contextualize phenomena so, i decided to do some research into why electrons spin, and it consequences.

I’ve spent pretty much the whole day trying to understand what causes the electron to spin, and what arises from it, but I still couldn’t find a satisfactory answer. At first, I read that the spin of electrons create the magnetic field of an atom, but then another page told me that it has little do with it. Then, there’s a whole thing that they don’t actually spin at all, which confused me even further.

To be frank I’m completely lost in the matter, and I would appreciate any direction as to Why and How the electron spins, and if the spin is what creates the magnetic field or not.

Thanks,

Terec

In: Physics

First off, the electron isn’t actually spinning. An electron isn’t a little sphere. “Spin” is a very unfortunate name because it doesn’t really have a physical analog that non-physicists can latch on to. Think if of it like charge…electrons have charge. It doesn’t really have a cause, it’s part of what being an electron *is*. Electrons have other properties too, like mass. Every electron has the same mass, every electron has the same charge.

Electrons also have angular momentum…this is where it gets weird because, in the macroscopic world, we associate angular momentum with spinning things. Down at the quantum level though, electrons just *have* angular momentum, just like they have mass and charge. We call that “spin”, in connection to the macroscopic equivalent we’re used to.

If you’re taking an introductory chemistry class, further research is going to be confusing because they tell us little lies in early chemistry to aid in our understanding. They clear it up in more advanced classes. For example, intro chemistry 101 says the protons of atoms never change.. a semester or 2 later you learn about nuclear radiation and proton emissions

Are you doing electron configuration with different shells?

think of spin as another dimension electrons move in. Remember the orbitals are electron clouds, its where you have the best chance of finding the electron, its not a rigid path. If you just need to understand to complete assignments, just remember spin directions must oppose in the same orbital/shell.. one up, one down, and so on.. electrons are negatively charged so they ALWAYS repel eachother.

Also, electrons are so small that they do not follow the laws of physics as you and I follow them. Talking about electrons goes extremely deep, people base entire degrees and careers on electrons and the theories get extremely complex.

If I knew what classes you’re taking I feel I could give you a better direction.. but consider this, my answer and your question are about subatomic particles, things going *within* a single atom/Molecule.

When talking about magnetism and electrons, like in physics, it’s referring to forces *between* 2 atoms or molecules..

Hope this helps! I used to tutor chemistry in undergrad

*This got a bit out of hand. If you want a tl;dr, spin is a quantum thing electrons have – you can think of it as a kind of mood electrons can be in, with two options, up and down (or 1/2 and -1/2). It has no non-quantum analogy or equivalent.*

———–

Spin is a property an electron can have. Like energy, or angular momentum.

Mathematically, spin acts like a kind of spinning. But it isn’t actual motion. It is sometimes called “intrinsic angular momentum.” Because it acts like spinning (but isn’t spinning), anything with electric charge that has spin will generate a magnetic field, as spinning charges generate magnetic fields.

Spin comes in either half number or whole numbers. An electron is a spin-1/2 particle. But confusingly this means that any one electron can have a spin of 1/2 or -1/2 (sometimes called “up” or “down”). You could think of this as spinning in different directions (except they’re not actually spinning, and there aren’t directions).

Most elementary particles are spin-1/2, but some are spin-1. So a photon is spin-1, meaning it can have a spin of 1, 0 or -1. Composite particles (and systems) can all sorts of different spin options. The Higgs Boson has a spin of 0. It is weird.

A spin-n particle can take spin values from n to -n in whole number steps. So a spin-3/2 particle could have spin 3/2, 1/2, -1/2, -3/2. A spin-3 particle could have spin 3, 2, 1, 0, -1, -2, -3.

You could think of these as being different “moods” a particle could have. They combine mathematically in interesting ways in combined systems, and fun quantum mechanics things happen with spin.

—————–

So, why does spin matter for electrons in atoms?

There is a rule that says no two identical fermions (things with half-integer spin like electrons, rather than whole-number spin) can be in the same *quantum state* in the same *quantum system*.

So inside a single atom you can’t have two (or more) electrons in the same state. This is why electrons in atoms come in shells. Each shell has so many “gaps” or states were an electron can be, and if you add in more electrons they have to find a gap to fit in – which might have to be in a higher shell.

But because electrons have two options for spin (spin up or spin down), for every state an electron can be in there is a second one with everything else the same but the opposite spin. This is why when drawing electrons in the energy shells we tend to draw them in pairs, and why there are always an even number of spaces in each shell.

For completeness, electrons in atoms have 4 different quantum numbers or properties like spin.

* *n*, the principle quantum number (corresponds to the shell or energy level) – can take any positive whole number (1, 2, 3…),
* *l*, azimuthal quantum number (corresponds to how it is spinning around the nucleus) – can take any whole number less than *n* (so for n = 2, can be 0 or 1) – you might have heard of s, p, d, f subshells, these are the *l* = 0, 1, 2, 3 options,
* *m*, the magnetic quantum number – which can take any whole number from +*l* to -*l* (so for *l* = 1 you can have *m* = -1, 0, 1),
* *s*, the spin – can be 1/2 or -1/2.

And no two electrons can take the same values for all 4 numbers. With a bit of logic we can see why we get the energy shells from the periodic table.

If *n* = 1, we must have *l* = 0, *m* = 0, and then *s* = 1/2 or -1/2. So we have two options (1,0,0,1/2) and (1,0,0,-1/2).

For the *n* = 2 energy shell, we can have *l* = 1, giving *m* = 1, 0, -1, or *l* = 0, giving *m* = 0, and then both spin options. This gives us 8 options in total:

> (2,1,1,1/2)

> (2,1,1,-1/2)

> (2,1,0,1/2)

> (2,1,0,-1/2)

> (2,1,-1,1/2)

> (2,1,-1,-1/2)

> (2,0,0,1/2)

> (2,0,0,-1/2)

Once we get above here things get a bit more complicated, but hopefully you get the general principle. The next layer we get 18 options, then 32 options, the 50 options and so on.

So if we have an atom and start throwing electrons at it, the first can take any spot (so will usually settle in one of the n = 1 slots). The second will take the second n = 1 slot. But then to throw in a third electron there is no longer any room in the n = 1 slot, so one of the electrons has to go to the n = 2 level, meaning we have to put in a bit more energy. And so on (the actual order electrons fill up all the slots is a bit complicated, but generally things will fill up lower levels).

Any system have angular momentum, around a pivot of choice. Spin is just angular momentum of a particle when considered alone.

Angular momentum are *not* the L=r x v from classical Newtonian mechanics. Instead, we define angular momentum by their main defining characteristic: it is preserved under all continuous rotations. The classical Newtonian angular momentum is a formula that give you a preserved quantity, assuming Newtonian physics is correct. But once we move into the weirder realm of quantum mechanics, we have to abandon the formula and stick with the most important property, the fact that it’s preserved under continuous rotations.

Given an arbitrary axis (this axis is normally named z), we can talk about angular momentum around this axis. This is a measurable number that is preserved under all continuous rotations around that axis. Due to funky issue with quantum physics, you can’t actually talk about angular momentum around all axis at the same time, because trying to measure this number around one axis disrupt the rest; in fact it’s not even possible to talk angular momentum about 2 axes at the same time. However, you can talk about magnitude squared of total angular momentum (when you consider rotation around ALL axis), which IS a number that can be measured.

Without loss of generality, we can assume that we do have a special z-axis where angular momentum exist, because this allows us to have an additional number to identify an electron: the secondary spin number.

If you consider one single particle by itself, this angular momentum give you the spin number, and the angular momentum around one specific z-axis give you the secondary spin number. For an electron, the spin number is fixed to be 1/2, so really you only care about secondary spin number. If you assume that there exist angular momentum around the z-axis, this 1/2 spin number – which tell you angular momentum – limit the possible value of angular momentum around the z-axis. By choosing 1 direction to be called “up” (associated with positive number) and the other direction “down”, we have 2 values +1/2 and -1/2. But warning: this “up” and “down” don’t have any actual geometric meaning, they are merely analogy from classical Newtonian mechanics where angular momentum is represented by a vector that can actually point up or down.

When you consider an atom together with an electron, the whole system itself have a different number that are also angular momentum (of the system). This is called total angular momentum. The electron, when considered alone, have its own angular momentum which is called spin. Subtracting the spin number from the total angular momentum give you orbital angular momentum. Since electron all have the same spin number, you only need orbital angular momentum and secondary spin number if you want to distinguish electrons by angular momentum.

Electrons don’t spin around the atom like the moon around the earth. Its similar to a swarm of bees next to a hive. Imagine a cloud where it’s location is probabilistic. It’s more likely to be in some places than others, but we can’t really pinpoint exactly where it will be.

Fundamental particles have fundamental properties . They can’t be explained in terms of other things, otherwise they wouldn’t be fundamental . All we can do is study what those properties do and how they behave. Spin is one of those fundamental properties .

Your book was right to say there is no “cause” for spin, although there certainly are consequences .

If you follow your physics teacher’s advice and always try to contextualise phenomena with analogies to ‘real’ things, you’re going to continue having a bad time with grasping quantum physics.
Asking what quantum phenomena ‘really’ are leads to a dead-end, because they don’t act like ‘real’ objects you can see, hold or draw.
One of the best things you can do in the subject is consciously avoid trying to think of analogies and mental models that use familiar concepts like thinking of electrons as little spinning balls. At this level they can hinder more than they help.
Concentrate on the mathematical rules and equations – think of electrons as a mathematical definition that happens to have some emergent ‘real-seeming’ properties if you look at them from a certain angle, rather than a real ‘thing’ that has mathematical rules attached.
Eventually once you are thoroughly familiar with the mathematics, you will have a new mental model of the electron that you can ‘imagine’, in a way, and not be wildly wrong. This is probably the best that a non-genius can hope for when understanding quantum physics!

I don’t really know the answer myself in terms of being able to “ELI5” but I did find this information over at stackexchange that explained it quite aptly:

https://physics.stackexchange.com/questions/418865/why-does-an-electron-have-spin

Furthermore: Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum.

I think the issue with spin is that it sounds like the emergent spinning-motion that we associate with a spinning top or something. There is a good reason why it’s called spin though.

In practice, I think its best to think about spin the same way to think about mass and charge. What exactly is mass? What exactly is charge? Its just intrinsic fundamental properties that things can have. Even though its quite hard to reduce them even further, we are pretty okay with talking about the mass and charge or a particle. The same should apply to spin.

Another way of thinking about spin is to just replace it with the words ‘angular momentum’, because that’s spin really is. Particles can have mass, momentum, charge, angular momentum, and there are some conservation laws/symmetries associated with those properties. Spin is part of angular momentum.

The fact that electrons don’t actually spin like a spinning top shouldn’t distract from the idea that spin is just another fundamental property of a particle. The reason why the picture is wrong is the same reason why the particle picture of an electron in an atom is wrong: the quantum mechanical wavefunction isn’t a particle.

Hopefully this helps to resolve some tension. I know it can be an unsatisfying answer, but I think it removes a lot of unnecessary confusion.

This video from veritasium covers most of your questions, but it is more eli15 than eli5.

https://youtu.be/v1_-LsQLwkA