Question

The nucleus of an atom can be assumed to be spherical. The radius of the nucleus of mass number A is given by $1.25\times {10}^{-13}\times A^{\frac{1}{3}}$ Radius of atom is one A . If the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is

• A. 1.0 X 10^-3
• B. 5.0 X 10^-5
• C. 2.5 X 10^-2
• D. 1.25 X 10^-13

Answer 1

The correct option is D

1.25 X 10^-13

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 = $1\dot{A}={10}^{-8}cm$.

$\frac{Volumeofnucleus}{Volumeofatom}=\frac{\left(\frac{4}{3}\right)\pi (5\times {10}^{-13}{)}^3}{\left(\frac{4}{3}\right)\pi ({10}^{-8}{)}^3}$

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