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  4. The ratio of the volume occupied by an atom to the volume of the nucleus is

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Q. The ratio of the volume occupied by an atom to the volume of the nucleus is

NTA AbhyasNTA Abhyas 2020Nuclei

Solution:

The radius of an atom $=I_{A}\approx 10^{- 10}m$
Radius of the nucleus $=I_{N}\approx 10^{- 15}m$
So, the ratio of their volumes is
$\frac{V_{A}}{V_{N}}=\frac{\frac{4}{3} \pi r_{A}^{3}}{\frac{4}{3} \pi r_{N}^{3}}$
$=\left(\frac{I_{A}}{I_{N}}\right)^{3}=\left(\frac{10^{-10}}{10^{-15}}\right)^{3}$
$\Rightarrow \, V_{A}:V_{N}=10^{15}:1$