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

Step1. Formula for volume of sphere

$\text{Volume of sphere}=\frac{4}{3}{\mathrm{\pi r}}^3$

Step2. Calculation of volume of atom

$$\begin{gathered} \text{Volume of atom=}\frac{4}{3}\text{π}{\left({10}^5{\mathrm{r}}_{\mathrm{n}}\right)}^3 \\ \text{=}\frac{4}{3}{\text{π10}}^{15}{\text{r}}_n^3 \end{gathered}$$

Step3. Ratio of sizes of atom to that of nucleus

Atomic size is represented in terms of atomic radius.

$$\begin{gathered} \text{Ratio of sizes of atom to that of nucleus=}\frac{\frac{4}{3}{\text{π10}}^{15}{\text{r}}_n^3}{\frac{4}{3}{\text{πr}}_n^3} \\ {\text{=10}}^{15} \end{gathered}$$

So, the ratio of their sizes is ${10}^{15}$.