Question

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

• A. $1.0 \times 10^{-3}$
• B. $5.0 \times 10^{-5}$
• C. $2.5 \times 10^{-2}$
• D. $1.25 \times 10^{-13}$

Answer 1

Answer: (D)

Radius of nucleus $=1.25 \times 10^{-13} \times(64)^{1 / 3}$

Radius of atom $=1 \, \mathring{A}=1 \times 10^{-8} \times 10^{-13} cm$

Fraction of volume

$=\frac{\text { Volume of nucleus }}{\text { Volume of atom }}$

$=\frac{\frac{4}{3} \pi\left(5 \times 10^{-13}\right)^{3}}{\frac{4}{3} \pi\left(1 \times 10^{-8}\right)^{3}}$

$=\frac{125 \times 10^{-39}}{10^{-24}}=1.25 \times 10^{-13}$