The radius of a nucleus of hydrogen is approximately [tex]r_{n1}=1\cdot 10^{-15}m[/tex], while we can use the Borh radius as the distance of an electron from the nucleus in a hydrogen atom: [tex]r_{e1}=5.3 \cdot 10^{-11}m[/tex]
The radius of a dime is approximately [tex]r_{n2} = 9\cdot 10^{-3}m[/tex]: if we assume that the radius of the nucleus is exactly this value, then we can find how far is the electron by using the proportion
[tex]r_{n1}:r_{e1}=r_{n2}:r_{e2}[/tex]
from which we find
[tex]r_{e2}= \frac{r_{e1} r_{n2}}{r_{n1}}= \frac{(5.3 \cdot 10^{-11}m)(9\cdot 10^{-3}m)}{1 \cdot 10^{-15}m}=477 m [/tex]
So, if the nucleus had the size of a dime, we would find the electron approximately 500 meters away.
