question_answer

The nuclear radius is of the order\[\text{1}{{0}^{-\text{13}}}\]cm while atomic radius is of the order\[\text{1}{{0}^{-\text{8}}}\]cm. Assuming the nucleus and the atom to be spherical, what fraction of atomic volume is occupied by the nucleus?

Answer:

Radius of nucleus \[({{r}_{n}})={{10}^{13}}cm\] Radius of atom \[({{r}_{a}})={{10}^{8}}cm\] Fraction of atomic volume occupied by nucleus \[=\frac{Volume\text{ }of\text{ }nucleus}{Volume\text{ }of\text{ }atom}=?\] Given that nucleus and atom are spherical. We know that, volume of a sphere\[=\frac{4}{3}\pi {{r}^{3}}\] Fraction of atomic volume occupied by nucleus \[(f)=\frac{{{V}_{n}}}{{{V}_{a}}}=\frac{\frac{4}{3}\pi {{({{10}^{-13}})}^{3}}}{\frac{4}{3}\pi {{({{10}^{-8}})}^{3}}}\] \[\Rightarrow \]\[f=\frac{{{V}_{n}}}{{{V}_{a}}}=\frac{{{10}^{-39}}}{{{10}^{-24}}}={{10}^{-15}}=\frac{1}{{{10}^{15}}}\]