As E=mc2 also E=F⋅s=r2kq⋅q⋅r Therefore dimensionally $\begin{aligned}
& \mathrm{mc}^2=\frac{1}{4 \pi \epsilon_0} \frac{\mathrm{q}^2}{\mathrm{r}} \
& \Rightarrow \mathrm{r}=\frac{\mathrm{e}^2}{4 \pi \epsilon_0 \mathrm{mc}^2}
\end{aligned}$
From the following, the quantity (constructed from the basic constants of nature), that has the dimensions, as well as correct order of magnitude, vis-a-vis typical atomic size, is:
Held on 9 Apr 2013 · Verified 6 Jul 2026.
4πε0mc2e2
me24πε0e2
4πε0b2me2
e24πε0mc2
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