Question

The ratio of the radii of hydrogen atom and its nucleus is $\text{~}{10}^5$.
Assuming the atom and the nucleus to be spherical,
(i) What will be the ratio of their sizes?
(ii) If the atom is represented by planet earth, ${}^{\prime }{R}_e^{\prime }=6.4\times {10}^{6}m.$ estimate the size of the nucleus.

Answer 1

(i) Let the radii of hydrogen by R and that of its nucleus be r.
The ratio of both the radii $\text{~}{10}^5$
$\Rightarrow \frac{R}{r}={10}^5$
Rearranging the above =
$\Rightarrow R={10}^{5}r$
Size of hydrogen atom
$=\frac{4}{3}\pi R^2$
$=\frac{4}{3}\pi ({10}^{5}r{)}^2$
Size of nucleus $=\frac{4}{3}\pi r^2$
Ratio of their volume $\frac{\frac{4}{3}\pi ({10}^{5}r{)}^3}{\frac{4}{3}\pi r^3}={10}^{15}$

(ii) Let the radii of hydrogen by $R_r$ and that of its nucleus be r.
The ratio of both the radii $\text{~}{10}^5$
$\Rightarrow \frac{R_e}{r}={10}^5$
Rearranging the above =
$\Rightarrow r=\frac{R_e}{{10}^5}$
Size of nucleus 'r' $=\frac{6.4\times {10}^{6}m}{{10}^5}=64m$