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# Atomic radius is of the order of $10^{-8} cm$ and nuclear radius is of the order of $10^{-13}$ cm. calculate what fraction of atom is occupied by nucleus?

$(a)\;10^{-14} \times V_{atom}\qquad(b)\;10^{-13} \times V_{atom}\qquad(c)\;10^{-15} \times V_{atom}\qquad(d)\;10^{-11} \times V_{atom}$

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A)
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Volume of nucleus = $\large\frac{4}{3}\pi r^3 = \large\frac{4}{3}\pi(10^{-3})^3 cm^3$
Volume of atom = $\large\frac{4}{3}\pi(10^{-8})^3cm^3$
$\large\frac{V_N}{V_{atom}} = \large\frac{10^{-39}}{10^{-24}}$
$V_{nucleus} = 10^{-15}\times V_{atom}$
Hence answer is (c)