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In the Rutherford's. nuclear model of the atom. the nucleus radius about \((10^{-15}\;m)\) is analogous to the sun about which the electron move in orbit radius \(({\approx}10^{-10}\;m\)  like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than actually it is? The radius of earth's orbit is about \(1.5\times 10^{11}\;m\) . The radius of sun is taken as \(7\times 10^8\;m.\)

Answer

The ratio of the radius of electron's orbit to the radius of nucleus is \(\frac{(10^{-10}\;m)}{ (10^{-15}\;m)}=10^5.\)  that is, the radius of the electron's orbit is \(10^5\)  times larger than the radius of nucleus. If the radius of the earth's orbit around the sun were \(10^5\)  times larger than the radius of the sun. the radius of the earth's orbit would be \(=10^5\times 7\times 10^8\;m= 7\times 10^{13}\;\mathit{m}\). This is more than \(100\) times greater than the actual orbital radius of earth.
Thus, the earth. would be much farther away from the sun. It implies that an atom contains a much greater fraction of empty space than our solar system does.
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