Question

The ratio of the volume occupied by an atom to the volume of the nucleus is

• A. $10^5:1$
• B. $10^{20}:1$
• C. $10^{15}:1$
• D. $1:10^{15}$

Answer 1

Answer: (C)

The radius of an atom $=I_A\approx 10^{-10}m$
Radius of the nucleus $=I_N\approx 10^{-15}m$
So, the ratio of their volumes is
$\frac{V_A}{V_N}=\frac{\frac{4}{3}\pi r_A^3}{\frac{4}{3}\pi r_N^3}$
$={\left(\frac{I_A}{I_N}\right)}^3={\left(\frac{10^{-10}}{10^{-15}}\right)}^3$
$\Rightarrow V_A:V_N=10^{15}:1$