Question

Question 37
The ratio of the radii of hydrogen atom and its nucleus is $\sim {10}^5$. Assuming the atom and the nucleus to be spherical.
(a) What will be the ratio of their sizes?
(b) If atom is represented by planet earth ${}^{\prime }{R}_e‘=6.4\times {10}^{6}m$, estimate the size of the nucleus.

Answer 1

(a)
Volume of a sphere with radius $r$ = $\frac{4}{3}\pi r^3$
Let R be the radius of the atom and r be that of the nucleus.
⇒ R = ${10}^{5}r$
Volume of the atom = $\frac{4}{3}\pi R^3$
$=\frac{4}{3}\pi {\left({10}^{5}r\right)}^3$
Volume of the nucleus = $\frac{4}{3}\pi r^3$
Ratio of the size of atom to that of nucleus = $\frac{R^3}{r^3}=\frac{{\left({10}^{5}r\right)}^3}{r^3}={10}^{15}$

(b) If the atom is represented by the planet earth,
Then the radius of the nucleus would be, $r_n=\frac{R_e}{{10}^5}$
$r_n=\frac{6.4\times {10}^6}{{10}^5}=64m$