Question

The nucleus of an atom is spherical. The relation between radius of the nucleus and mass number $A$ is given by $1.25\times 10^{-13}\times A^{\frac{1}{3}}cm$ . If radius of atom is one $\mathring{A}$ and the mass number is $64$ , then the fraction of the atomic volume that is occupied by the nucleus is $\left(x\right)\times 10^{-13}$ . Calculate $20x$ (nearest integer).

Answer 1

Answer: 25

Radius of nucleus $=1.25\times 10^{-13}\times A^{\frac{1}{3}}cm$
$=1.25\times 10^{-13}\times 64^{\frac{1}{3}}=5\times 10^{-13}cm$
Radius of atom $=1\mathring{A}=10^{-8}cm$.
$\frac{\text{ Volume of nucleus }}{\text{ Volume of atom }}=\frac{\left(\frac{4}{3}\right)\pi {\left(5\times 10^{-13}\right)}^3}{\left(\frac{4}{3}\right)\pi {\left(10^{-8}\right)}^3}$
$=1.25\times 10^{-13}.$