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I have recently learnt about atomic structure and the Bohr model of the atom and have observed a discrepancy between it and my previous knowledge based on physics.

For simplicity, assume the atom is of hydrogen.

Total energy of electron $$E= -13.6 \left(\frac{z^2}{n^2}\right) \pu{eV/atom}$$ where $z$ is atomic number, $n$ is energy level.

Thus, at $n=\infty$, $E=0$.

Now, by the relation Total Energy = potential energy/2 (from $TE=-KE=PE/2$),

$$PE=0/2$$ so $$PE=0$$

Now, the infinite energy level ($n=\infty$) occurs at a finite distance from nucleus (as the difference in distance between the energy levels decreases at higher energy levels).

Thus, $PE=0$ at a finite distance from the nucleus.

But, I have previously studied that $PE$ of a system of a negative charge (electron) and positive charge(nucleus) is $=0$ only at an infinite distance.

Thus, the discrepancy.

Please let me know where I have gone wrong.

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  • $\begingroup$ You incorrectly assume that when $n=\infty$ the electron and proton are at a finite separation. $\endgroup$ – porphyrin Jun 1 at 8:19
  • $\begingroup$ Let's forget for a moment that the Bohr model is pretty rudimentary. Why do you think that the orbital radius for n-> infinite is finite? Can you explain this a little more so we can answer? $\endgroup$ – Greg Jun 1 at 8:24
  • $\begingroup$ Please see the following image: google.com/…: $\endgroup$ – Shashwat Tomar Jun 1 at 8:29
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    $\begingroup$ Yes your question is clear, and clearly based on a wrong premise. You know the formula for energy; you plug $n=\infty$ and correctly deduce that $E=0$. But you don't know the formula for radius and can't plug $n$ there, so you have to rely on obscure googled pictures instead. That's the root of all evil. $\endgroup$ – Ivan Neretin Jun 1 at 9:04
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    $\begingroup$ The picture is not obscure, it is a great representation of the relationship between n and E in the H atom. However, it has nothing to do with radius. The distances shown between the bars are not spatial distances, they represent the energy differences. The vertical axis is energy. $\endgroup$ – electronpusher Jun 1 at 17:30

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