The ratio of the radii of hydrogen atom and its nucleus is $~ {10}^5$ . Assuming the atom and the nucleus to be spherical. What will be the ratio of their sizes?

The ratio of their sizes will be equal to ${10}^{15}$.
Atomic size or radii is defined as the distance between nucleus and valence shell of an atom.
Ratio of radii of hydrogen and its nucleus,  $\frac{r_H}{r_n}={10}^5$
Volume of sphere $=\frac{4}{3}\pi r^3$
Therefore, volume of hydrogen atom $=\frac{4}{3}\pi {r_H}^3$
Volume of nucleus of hydrogen $=\frac{4}{3}\mathit{ \pi }{r_n}^3$
Thus, ratio of volumes $=\frac{\frac{4}{3 }\pi {r_H}^3}{\frac{4}{3}\pi {r_n}^3}$ = $\left(\frac{r_H}{{\mathit{rn}}_{ }}\right)$
$= (10^5{)}^3$
$= 10^{15}$
 Therefore, the ratio of their sizes will be ${10}^{15}$.