• # question_answer The nucleus of an atom can be assumed to be spherical. The radius of the nucleus of mass number $A$ is given by $1.25\times {{10}^{-13}}\times {{A}^{1/3}}cm$ Radius of atom is one ${AA}$. If the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is [NCERT 1983] A) $1.0\times {{10}^{-3}}$              B) $5.0\times {{10}^{-5}}$C) $2.5\times {{10}^{-2}}$              D) $1.25\times {{10}^{-13}}$

Radius of nucleus $=1.25\,\times {{10}^{-13}}\times {{A}^{1/3}}\,cm$                   $=1.25\,\times {{10}^{-13}}\times {{64}^{1/3}}$$=5\times {{10}^{-13}}\,cm$                    Radius of atom = $1\text{{ }\!\!\mathrm{AA}\!\!\text{ }}\,={{10}^{-8}}cm.$                    $\frac{\text{Volume of nucleus}}{\text{Volume of atom}}$$=\frac{(4/3)\pi \,{{(5\times {{10}^{-13}})}^{3}}}{(4/3)\pi \,{{({{10}^{-8}})}^{3}}}$                                 $=1.25\,\times {{10}^{-13}}$.