(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
*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.*
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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.
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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).
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