In Rutherford’s nuclear model of the atom, the radius of the nucleus is about \(10^{-15}\ \mathrm{m}\) and the radius of the electron orbit is about \(10^{-10}\ \mathrm{m}\). Suppose the atom is enlarged in the same proportion until its nucleus is as big as a marble of radius 1 cm. The radius of the electron orbit would then be about
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1 km
When the atom is enlarged in the same proportion, the ratio of the two radii stays the same. So first find how many times larger the electron orbit is than the nucleus.
\( \begin{aligned} \frac{r_{\text{orbit}}}{r_{\text{nucleus}}} &= \frac{10^{-10}}{10^{-15}} \\ &= 10^{5} \end{aligned} \)
\( \begin{aligned} r_{\text{orbit}} &= 10^{5}\times1\ \mathrm{cm} \\ &= 10^{5}\ \mathrm{cm} \\ &= 1\ \mathrm{km} \end{aligned} \)
Hence, the electron would go round the marble at a distance of about 1 km. Most of the atom is empty space.
NCERT (2026-27):
Example 12.1 – “… The ratio of the radius of electron’s orbit to the radius of nucleus is (10–10 m)/(10–15 m) = 105, that is, the radius of the electron’s orbit is 105 times larger than the radius of nucleus. …”