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The Heisenberg's uncertainty principle prevents us from measuring the position and momentum of an electron accurately at the same time. But that is just our inability, right?

In reality, would electrons be revolving in fixed orbits like in Bohr's model?

Even if electrons have wave nature, does the maximum of the wave revolve in an orbit like an electron in Bohr's model?

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  • $\begingroup$ You may be interested in the Ehrenfeat theorem. See en.m.wikipedia.org/wiki/Ehrenfest_theorem $\endgroup$ – my2cts Apr 11 at 7:45
  • $\begingroup$ Thanks but that page is a little complicated for me.. I'm a highschool student. So I won't understand the mathematics of it. I'm just curious. $\endgroup$ – Michael Faraday Apr 11 at 7:55
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    $\begingroup$ An electron in an $s$ orbital has zero orbital angular momentum, its momentum is purely radial. That's hard to reconcile with Bohr's model, or a classical orbit. $\endgroup$ – PM 2Ring Apr 11 at 7:58
  • $\begingroup$ @PM2Ring It is hard to reconcile with a classical circular orbit , but less hard with a radial one. $\endgroup$ – my2cts Apr 11 at 8:04
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    $\begingroup$ @my2cts Fair enough, but a classical radial trajectory doesn't sit well with the spherically symmetric distribution of the position of an $s$ electron. $\endgroup$ – PM 2Ring Apr 11 at 8:08
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Not a theoretical physicist here, so I may not be updated on the fanciest interpretations of quantum mechanics, but I will try to answer to your questions in order

  1. Actually one has not to confuse the uncertainty principle with the observer effect. The latter tells you that when you measure something in quantum mechanics, you make its wave function collapse, or in simpler words you “destroy” it. If you repeat the measurement you will always get the same value. The uncertainty principle, however, is an intrinsic limit and it is common to any wave-like system. It is not related to the act of making a measurement and it will be there even if we have a perfect instrument to make the measurement. For example the uncertainty principle applies to every conjugate quantities, such as position and momentum (the most famous one), energy and time, and so on. It is possible to be convinced of the fact that the phase of an electromagnetic wave and the number of photons measured are also conjugated quantities: the more photons we measure, the more accurately we estimate the phase of the EM wave composed by those photons. Suppose that we have a perfect photo-detector and we measure all the photons incoming: if the EM wave has weak intensity and thence only few photons reach us, we will not give a good estimate of the phase of the EM radiation (we will have a big uncertainty) even if our detector is on the paper perfect.
  2. According to the most common interpretation, electrons do not move on orbits, but rather they are distributed around the nucleus. We call orbitals the probability density functions which tells us where it is most likely to find the electrons. Bohr model was the precursor of our current models and had quite some success in explaining some phenomena, but now we have more refined theories.
  3. The peak of the probability density I mentioned before is where it is most likely to find the electron at a given time.
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  • $\begingroup$ Uncertainty principle is an intrinsic limit? Suppose you have an electron moving in space with some momentum (and not influenced by any forces). The electron is actually moving a definite path right? $\endgroup$ – Michael Faraday Apr 11 at 9:46
  • $\begingroup$ @michaelFaraday a free electron can be seen as a wave packet. The broader the packet is, the more uncertainty there is on its position. If I have a rather broad packet (lots of uncertainty) in the coordinates space, in the Fourier or momentum space I will have quite a narrow packet (way less uncertainty on momentum). The uncertainty principle could arise also as a property of Fourier transform. $\endgroup$ – Davide Dal Bosco Apr 11 at 10:50
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It is not our inability to measure a position of electron with absolute certainty but a natural behavior of elementary particles.

Electrons in atom do not orbit a atom nucleus but they appear around it in more or less random fashion. However, this randomness is governed by a probability distribution.

The probability is graphicaly ilustrated by so-called orbitals. As you can see from pictures in the link, orbitals with higher principal number $n$ are far from being circular like in Bohr's model.

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