(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
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.
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