Question

please answer me the above question with proper explanation it's ver urgent

Answer 1

Let the radius of nucleus, r = 10^(-13) cm

volume of nucleus =
$\frac{4}{3} \pi {r}^{3} = \frac{4}{3} \pi {( {10}^{ - 13}) }^{3} = \frac{4}{3} \pi ({10}^{ - 39} ) \: {cm}^{3}$
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radius of atom, r = 10^(-8) cm

volume of atom =

$\frac{4}{3} \pi {r}^{3} = \frac{4}{3} \pi {( {10}^{ - 8}) }^{3} = \frac{4}{3} \pi ({10}^{ - 24} ) \: {cm}^{3}$
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nucleus as fraction of atomic volume:

$fraction = \frac{ volume \: of \: nucleus}{volume \: of \: atom}$

$= \frac{ \frac{4}{3}\pi \times {10}^{ - 39} }{ \frac{4}{3}\pi \times {10}^{ - 24}} \\ \\ = \frac{ {10}^{ - 39} }{ {10}^{ - 24} }$

$= {10}^{ - 39 + 24} \\ \\ = {10}^{ - 15}$

Hence the nucleus occupies a tiny fraction of the atomic volume. It occupies ${10}^{ - 15}$ or $\frac{1}{ {10}^{15} }$ of the atomic volume.