Question

The nuclear radius is of the order of $10^{-3}\, cm$ while atomic radius is of the order $10^{-8}\, cm$. Assuming the nucleus and the atom to be spherical, the fraction of the atomic volume occupied by the nucleus is

• A. $10^{-15}$
• B. $10^{-10}$
• C. $10^{-13}$
• D. $10^{-14}$

Answer 1

Answer: (A)

The volume of a sphere $= 4\pi r^{3}/3$, where $r$ is the radius of the sphere.
$\therefore $Volume of the nucleus $=4 \pi r^{3}/3$
$4\pi (10^{-13})^3/{3} \,cm^{3}$
Similarly, volume of the atom $=4\pi r^{3} /3 = 4\pi (10^{-8})/3 \,cm^{3}$ Fraction of the volume of atom occupied by the nucleus
$= \frac{4\pi \left(10^{-13}\right)^{3} /3 cm^{3}}{4\pi\left(10^{-8}\right)^{3} /3cm^{3}} =10^{-15}$