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We're told that charge is quantized. That the charge any body carries has to be an integral multiple of the fundamental unit of charge: $e=1.602×10^{-19}C$ such that $q=ne$ where $n$ is an integer.

But my book says (while explaining van der Waals forces) that the partial charges on a molecule ($\delta$) are always less than the fundamental unit of charge $e$.

How can this be? Isn't this against the quantization condition for charges?

Edit

enter image description here

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  • $\begingroup$ Minor comment to the post (v3): Please consider to mention explicitly author, title, etc. of textbook, so it is possible to reconstruct link in case of link rot. $\endgroup$
    – Qmechanic
    Apr 11 '17 at 6:06
  • $\begingroup$ Related question on Chemistry StackExchange : Does partial charge violate the law of quantization of charge? $\endgroup$
    – Vishnu
    Feb 1 '20 at 7:33
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Imagine that you live in a world where the fundamental particles are cones with mass 1. But at some moment you want to know the weight of the halfs (the tip and the basis). Nobody forbids to calculate this masses. And this could be useful to calculate vibrations and rotations of such fundamental particles.

So it makes sense to calculate the charge distribution in molecules and it's not surprising that the calculations of this distribution are not integers of the fundamental electric charge q.

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The partial charges which are referred to in the textbook do not exist. They are just an analogy used to compare molecular dipoles with macroscopic dipoles (two charges $\pm q$ separated by some distance $d$).

As the diagram on the left points out, these charges are actually an asymmetry in the distribution of the electrons in the molecule, so that there is a difference between the centres of +ve and -ve charge, creating an electric dipole moment.

The formula for dipole moment is $p=qd$. If we take $d$ as the distance between the two nuclei in a molecule, then $q$ will be a small fraction of the electronic charge. However, if we take $q$ to be the total charge on all $n$ electrons in the molecule, then $q=ne$ is large and $n$ is a whole number. In this view it is actually $d$ - the separation between the centres of +ve and -ve charge - that is a small fraction of the inter-nuclear distance.

Either way you look at it (small $q$ & large $d$ or large $q$ & small $d$) the value of $p=qd$ is the same, and it is this value which is important, not the values of $q$ or $d$.

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