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As a pretense, my understanding of chemistry extends only to a high school honors level.

As I know it, electrons occupy orbitals in which they could possibly be situated, and constantly move around those orbitals by their attraction to the nucleus and repulsion to each other.

Why is it that this specific arrangement should happen? Wouldn't it make more sense that, since they are attracted to the nucleus and repulsed by each other, they find some sort of arrangement where they are all static and the same distance away from the nucleus and an equal distance away from each other (IE, they form one big s-shaped orbital and occupy it such that they are all equally as far away from each other as possible while also being equally as close to the nucleus as possible)?

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    $\begingroup$ It is all very different from what you are imagining, and different from its opposite, too. There is no motion, no arrangement, not even distance. Trust me, there is no point even to think of it before you start learning real quantum mechanics. $\endgroup$ Mar 8 at 22:44
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    $\begingroup$ Is chemistry about what makes electrons, well, electrons? Not really... $\endgroup$
    – Mithoron
    Mar 9 at 2:10
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    $\begingroup$ Ignore Ivan's comment, in which he's effectively saying "don't worry your pretty little head about it" until you're taking upper-div QM. He's essentially saying it's all so mysterious and over-your-head that, as a h.s. student, there's no point in even trying to think about QM. That's both condescending and patently false. There are many ways that h.s. students can start developing an intuition about QM, using analogies like standing waves on strings. So don't let comments like this discourage you. It's a disservice for this site to be telling curious students to put their curiosity on hold. $\endgroup$
    – theorist
    Mar 9 at 4:36
  • $\begingroup$ For instance, here are youtube videos in which experts show that both higher dimensions and quantum computing can be explained at multiple levels, from child to teen to college student to grad student to expert: youtube.com/watch?v=3KC32Vymo0Q and youtube.com/watch?v=OWJCfOvochA $\endgroup$
    – theorist
    Mar 9 at 4:36
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    $\begingroup$ According to Earnshaw's theorem, a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. $\endgroup$
    – Poutnik
    Mar 9 at 8:24
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The uncertainty principle and the impossibility of stable static structures

I could say "it's all quantum stuff, wait until you are taught that" but there are good ways to grasp the key ideas without all the highly mathematical detail that comes with that level of understanding.

Two things matter. Even if we assume no quantum effects there is no arrangement of static electrons that can be stable. There is a mathematical derivation of this (as @Poutnik points out this is Earnshaw's Theorem) but the intuition is similar to the observation that a planetary system with no motion can't be stable (though gravity only attracts). Or the observation that a mechanical system with a rigid rotating object (say a hula hoop) won't stay stable unless there is both pulling a pushing from a central point (it looks stable until there is any fluctuation away from a perfect circular orbit when the fluctuation is amplified by the pull to the centre).

The second thing that matters is the Heisenberg uncertainty principle. It is possible to understand the implication without needing the grasp the math. In simple terms there is a limit to the precision of knowledge about both momentum and position: if we know exactly where something small is our knowledge about how fast it is moving must be very imprecise (strictly speaking this is more than a limit on our knowledge: it is a fundamental limit on reality). We can't have static electrons: if we knew where they were, they would be moving at some indefinite speed. The implication of the math is that only certain combinations of momentum and spatial coordinates are possible (we call them orbitals and they represent regions of probability of finding electrons). Like a vibrating string, only certain specific modes of vibration are possible. Unlike a string there are no modes where everything is static.

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  • $\begingroup$ So what you're saying is that there's no use visualizing it, it's based off of theoretical reasoning and math? $\endgroup$
    – Paulemic
    Mar 9 at 21:18
  • $\begingroup$ @Paulemic there are some physical analogies as to why some systems can't be stable. But heisenberg stuff doesn't have many good analogies on the macro-scale (unless you understand fourier transforms in which case vibrating strings illustrate the trade-off between frequency specificity and time resolution well: a string has to vibrate for an infinite time to have a very precise frequency; a short time slice inevitably has a fuzzy frequency in a way very similar to the momentum/location tradeoff for quantum systems)... $\endgroup$
    – matt_black
    Mar 9 at 21:24
  • $\begingroup$ @Paulemic ...but it is wrong to say it is all about theoretical reasoning and math. This is what we observe to be true for very small things. The theory is subordinate to the observations. $\endgroup$
    – matt_black
    Mar 9 at 21:25
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Wouldn't it make more sense that, since they are attracted to the nucleus and repulsed by each other, they find some sort of arrangement where they are all static and the same distance away from the nucleus and an equal distance away from each other (IE, they form one big s-shaped orbital and occupy it such that they are all equally as far away from each other as possible while also being equally as close to the nucleus as possible)?

What you are suggesting here is a static equilibrium of many particles. It would be similar (but not equivalent to, because of all sorts of issues) to a pebble tower or balancing a razor-thin object on its razor-thin side: inherently unstable. As soon as you accidentally as much as move a nucleus further away, the entire system would no longer be in equilibrium as the electric field changes; the first particle would start moving, changing the electric field again and so on until complete chaos.

This isn't a stretch of imagination either: with every movement my fingers are making, tons of atoms are moving closer to and further away from each other meaning any type of static equilibrium wouldn't last a femtosecond.

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According to the Heisemberg principle, it is not possible to know with an arbitrary precision the values of two observables whose operators do not commute.

According to QM, every physical property, like energy, is associated to an operator. An operator is not black magic, it is a mathematical being that does things, like the addition operator $+$.

Two operators $\hat{A}$ and $\hat{B}$ do not commute is $\hat{A}\hat{B} \ne \hat{B}\hat{A}$. Like with matrices.

If you do some paper and pencil calculations, momentum, therefore velocity, and position of a particle are observables whose operators do not commute. Then, from a micorscopic point of view you cannot know at the sime time both velocity and position of an electron. In fact, an orbital is a probabilistic concept: it is the space region in which the electron has the 95% probability to be found. The "continous motion" of an electron is just a consequence of the Heisemberg principle.

I suggest you the magnificient divulgative book of Paul Halpern "The quantum labyrinth".

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