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Specifically, Bohrs atom model gives the radius of an atom as 0.53‎Å, while a quantum description offers a similar value. What is the difference between these?

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    $\begingroup$ Quantum description does indeed offer the same value, but in a very different context. It is not the literal "size" of the atom, to begin with. Atoms don't have definite sizes at all. $\endgroup$ – Ivan Neretin Feb 2 '17 at 12:34
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    $\begingroup$ Your statement is mostly true for hydrogen - but for other atoms, the Bohr model does not work quantitatively. $\endgroup$ – TAR86 Feb 2 '17 at 12:35
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    $\begingroup$ May be useful: chemistry.stackexchange.com/questions/59096/… $\endgroup$ – Felipe S. S. Schneider Feb 2 '17 at 12:41
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    $\begingroup$ related chemistry.stackexchange.com/questions/28659/… $\endgroup$ – Mithoron Feb 2 '17 at 12:42
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    $\begingroup$ this is because quantum model offers a possibility of finding an electron somewhere, so when the radius of an atom is measured the average distance is taken $\endgroup$ – phenolicdeath Feb 2 '17 at 15:10
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The Bohr model is a comparatively simple model, whereas the quantum description is part of the huge theory of quantum mechanics, so to list all the differences including implications would need to explain quantum mechanics itself.

But I think quite a good starting point would be to say, the Bohr model has electrons travel on certain, specific, classical trajectories, picked out by certain rules. The quantum model does not have electron trajectories. Instead electrons are quite different, they are spread out a bit like clouds of gas, in areas called atomic orbitals. I would recommend reading about atomic orbitals, the Wikipedia page is quite interesting. You will see very quickly they are quite different from the Bohr model.

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  • $\begingroup$ Orbitals are not "areas of occupied space"! Such statements repeatedly lead to wrong impressions about quantum mechanics. They are wave functions describing the electron itself, not just where it is. $\endgroup$ – Feodoran Sep 19 '18 at 14:49
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    $\begingroup$ @Feodoran yes, orbitals carry more than position information, with the phases you also get momentum information. Could you please give me an idea of the wrong impression this kind of answer leads to? I can then reformulate it to avoid this. Because of the scope of the question and the asker not apparently having any knowledge of quantum mechanics, it doesn't seem to me like the extra complexity of addressing phase properties would be worth the added information. If you could give a phrasing that explains these details clearly to a lay person I may include it in my answer. $\endgroup$ – user183966 Sep 19 '18 at 21:13
  • $\begingroup$ There is no easy phrasing, that's why people keep using the "occupied space" thing. What about "In the quantum model electrons are not considered to be particles anymore, but are typically described by an abstract wave functions (orbitals)."? One would need to explain now what a wave function actually is, but this would lead to explaining all the basics behind QM, as you already noted. $\endgroup$ – Feodoran Sep 19 '18 at 22:55
  • $\begingroup$ About the wrong impressions: A classical particle moving around in some area can be described by a trajectory. Averaging the positions of this trajectory over time will lead to probability distribution of that classical particle. Just stating that in QM orbitals are "areas of occupied space" does not contradict that classical description. And I think many people will imagine it like this, since they are trying to hang on to the particle picture. It should be made more clear that QM does not work like this. The explanation should include arguments that directly contradict the particle picture. $\endgroup$ – Feodoran Sep 19 '18 at 23:04
  • $\begingroup$ @Feodoran ok, I have changed my wording to hopefully make the situation clearer. $\endgroup$ – user183966 Sep 19 '18 at 23:38

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