3 ms·

This cloud of probability you're talking about - is it different from the cloud of probabilities of electron's position relative to the atomic nucleus?

by p1esk 4y ago

wiml 4y ago
The cloud of probable location is the magnitude of the electron's wavefunction, as I understand it. So they're the same thing, but there's extra information in there too beyond simply position (wavefunctions are complex-valued, not real-valued). Source: Dimly remembered undergrad physics.
scotty79 4y ago
It's the same thing for electron that freely propagates as for the one bound, for example inside atom or a molecule. It's just that the shape is different. I think it's worth mentioning it's not exactly a probability understood as a theoretical chance of something being somewhere. This wave function is what actually is the physical reality. But we can't measure this reality without interacting with it and when we do interact multiple times and interpret those interactions as if they were caused by pointlike particle being in particular spot then we see that results of those interactions have distribution matching this "probability" "cloud" (square of a wave function).
- p1esk 4y ago
  I'm curious what would it look like if we could expand the size of an atom by a billion times, preserving all its quantum properties.
  - scotty79 4y ago
    If you want to see how electron (wave function) can look when it's stuck to a nucleus check out orbital shapes: https://www.google.com/search?q=orbital+shapes https://www.google.com/search?q=orbital+shapes As more and more electrons get stuck to nucleus it gets crowded around it so further electrons form more and more bizarre shapes of larger and larger sizes as only two electrons can stably fit in a single specific shape of a specific size (Pauli exclusion principle). They do it by taking opposite spins.
    - scotty79 4y ago
      Although things are not that easy and ordered.... You can look at simulated orbitals here: https://falstad.com/qmatom/ https://falstad.com/qmatom/ s-orbitals are spherically symmetrical. You might convince yourself that p-orbitals are also fine, because 3 of them in 3 dimensions do have reasonable rotational symmetry. You'll notice that when you move to d-orbitals things start to get really weird. 4 of them are fairly equivalent but it turns out that you can cram 10 electrons of this energy around the nucleus in this fashion. So there are 5 d orbitals. And we can't really fit the fifth in similar manner as other 4. https://profound-advice.com/what-is-the-difference-between-the-dxy-and-dx2-y2-orbitals/ https://profound-advice.com/what-is-the-difference-between-t... Check the video. So while we technically have 5 d orbitals, one of them is weird. Its weirdness is an artifact of math. To get the orbitals we are solving Schrodinger equation in spherical coordinates, where one axis is chosen as special. This gives us this weird solution. https://chemistry.stackexchange.com/questions/117243/why-is-there-a-z%c2%b2-label-for-d-orbitals-but-no-x%c2%b2-and-y%c2%b2-labels-with-correspondi https://chemistry.stackexchange.com/questions/117243/why-is-... Physical reality can't depend on our choice of coordinate system so this tells us that orbitals as we draw them don't really directly express the physical reality. In actual physical reality all five of d orbitals have the same shape (somewhere in between the nice d and weird d), but since we can't tell the difference between electron on one d orbital from the electron on another then as long as all 5 orbitals sum up to physical reality our math still works, even if we choose to decompose the solution into 5 non-rotationally-symmetrical parts to make math easier on ourselves.

This cloud of probability you're talking about - is it different from the cloud of probabilities of electron's position relative to the atomic nucleus?

by p1esk 4y ago

This cloud of probability you're talking about - is it different from the cloud of probabilities of electron's position relative to the atomic nucleus?

wiml 4y ago

The cloud of probable location is the magnitude of the electron's wavefunction, as I understand it. So they're the same thing, but there's extra information in there too beyond simply position (wavefunctions are complex-valued, not real-valued). Source: Dimly remembered undergrad physics.

scotty79 4y ago

It's the same thing for electron that freely propagates as for the one bound, for example inside atom or a molecule. It's just that the shape is different. I think it's worth mentioning it's not exactly a probability understood as a theoretical chance of something being somewhere. This wave function is what actually is the physical reality. But we can't measure this reality without interacting with it and when we do interact multiple times and interpret those interactions as if they were caused by pointlike particle being in particular spot then we see that results of those interactions have distribution matching this "probability" "cloud" (square of a wave function).

p1esk 4y ago
I'm curious what would it look like if we could expand the size of an atom by a billion times, preserving all its quantum properties.
- scotty79 4y ago
  If you want to see how electron (wave function) can look when it's stuck to a nucleus check out orbital shapes: https://www.google.com/search?q=orbital+shapes https://www.google.com/search?q=orbital+shapes As more and more electrons get stuck to nucleus it gets crowded around it so further electrons form more and more bizarre shapes of larger and larger sizes as only two electrons can stably fit in a single specific shape of a specific size (Pauli exclusion principle). They do it by taking opposite spins.
  - scotty79 4y ago
    Although things are not that easy and ordered.... You can look at simulated orbitals here: https://falstad.com/qmatom/ https://falstad.com/qmatom/ s-orbitals are spherically symmetrical. You might convince yourself that p-orbitals are also fine, because 3 of them in 3 dimensions do have reasonable rotational symmetry. You'll notice that when you move to d-orbitals things start to get really weird. 4 of them are fairly equivalent but it turns out that you can cram 10 electrons of this energy around the nucleus in this fashion. So there are 5 d orbitals. And we can't really fit the fifth in similar manner as other 4. https://profound-advice.com/what-is-the-difference-between-the-dxy-and-dx2-y2-orbitals/ https://profound-advice.com/what-is-the-difference-between-t... Check the video. So while we technically have 5 d orbitals, one of them is weird. Its weirdness is an artifact of math. To get the orbitals we are solving Schrodinger equation in spherical coordinates, where one axis is chosen as special. This gives us this weird solution. https://chemistry.stackexchange.com/questions/117243/why-is-there-a-z%c2%b2-label-for-d-orbitals-but-no-x%c2%b2-and-y%c2%b2-labels-with-correspondi https://chemistry.stackexchange.com/questions/117243/why-is-... Physical reality can't depend on our choice of coordinate system so this tells us that orbitals as we draw them don't really directly express the physical reality. In actual physical reality all five of d orbitals have the same shape (somewhere in between the nice d and weird d), but since we can't tell the difference between electron on one d orbital from the electron on another then as long as all 5 orbitals sum up to physical reality our math still works, even if we choose to decompose the solution into 5 non-rotationally-symmetrical parts to make math easier on ourselves.