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

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}} $
$=1.25 \times 10^{-13} .$