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Are they thought to continuously pop in and out of existence at various points inside the orbital defined by probabilities or do they follow definite paths that are made fuzzy by the Heisenberg uncertainty principle? I sometimes find myself as thinking of the electron cloud as a gas with varying charge density corresponding to the shape of the atomic orbital.

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    $\begingroup$ Take look HERE I hope you will get complete idea $\endgroup$ – Freddy Jun 13 '14 at 7:11
  • $\begingroup$ if you don't like to read then search it on YOUTUBE $\endgroup$ – Freddy Jun 13 '14 at 7:13
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    $\begingroup$ Don't 'picture' it, your intuition will not work here. Quantum mechanics does not include such word as 'trajectory', meaning that common understanding of movement is absolutely useless in understanding of electone movement. The most understandable concept applicable here is idea of 'electronic density', i.e. how much electrons is located in region of space, i.e. your concept is not all that wrong. $\endgroup$ – permeakra Jun 13 '14 at 12:17
  • $\begingroup$ Related post physics.stackexchange.com/questions/115188/… $\endgroup$ – user26143 Jun 13 '14 at 12:49
  • $\begingroup$ chemistry.stackexchange.com/questions/42032/… $\endgroup$ – Mithoron Nov 27 '16 at 19:34
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I think you miss an important notion to get a better understanding of the behavior of the electrons: wave-particle duality. I believe that a better visualization takes into account that you have to deal even with a wave. From what you say it seems that your picture is shifted only to the particle-side, keep meditating for a half an hour trying to visualize the electron as a wave. For me is a very interesting mind experiment. Then move to the orbital concept.

At Lund University researches took a picture of a moving electron. This image maybe could be helpful for your meditation:

captured electron movement

Lund University. "Electron Gets Film Debut In First-ever Video Of Its Kind." ScienceDaily. ScienceDaily, 25 February 2008. www.sciencedaily.com/releases/2008/02/080222095358.htm.

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The interpretation of quantum mechanics is an unresolved issue in physics and philosophy.

I sometimes find myself as thinking of the electron cloud as a gas with varying charge density corresponding to the shape of the atomic orbital.

This was Schrodinger's original interpretation when he developed/postulated the Schrodinger equation, that the wave function should be interpreted as charge density. However, the Copenhagen interpretation soon became most popular. The Copenhagen interpretation associates the wavefunction with a probability distribution rather than a charge distribution.

Are they thought to continuously pop in and out of existence at various points inside the orbital defined by probabilities or do they follow definite paths that are made fuzzy by the Heisenberg uncertainty principle?

The electrons of atoms do not pop in and out of existence. However, virtual electrons pop in and out of existence and can affect the energy levels of atoms slightly, for example contributing to the Lamb shift.

According to the Copenhagen interpretation, the electrons do not follow definite paths; however, there are other interpretations which have not been disproven, such as Bohmian Mechanics where definite paths are followed.

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I hear you. I have been struggling with trying to visualize it as well. The problem is that when we get down to this world of quantum effects, stuff stops being easy to visualize just on the basis of pure weirdness. Whomever in the comments said "don't visualize it" is basically correct. But here goes anyway, following good advice is optional =)

I did however have some epic a-ha moments when I saw the models of vibration modes of circular drums. Especially as you go up in modality - it is fascinating to see the vibration mode $u_{21}$ and then think of the 3d orbital shape.

The Heisenberg uncertainity principle basically arises when we need to for instance pinpoint the exact location of the electron (how can momentum be preserved when we reduce the drums' surface area down to a point) - For me it is always easier to think of the electron as smeared out over a surface (or, better yet a space) until we actually try to locate it - at which point it will coalesce into a particle.

Disclaimer: All of this is factually B.S. - the only model that can accurately represent any single part or property of the universe - is the universe.

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