Question

The ratio of the volume of the atom to the volume of the nucleus is of the order of

• A. $10^{10}$
• B. $10^{15}$
• C. $10^{20}$
• D. $10^{25}$

Answer 1

Answer: (B)

Radius of the atom, $R_a=1\mathring{A}=10^{-10}m$
Volume of the atom, $V_a=\frac{4}{3}\pi R_a^3=\frac{4}{3}\times \pi \times {\left(10^{-10}\right)}^3{m}^3$
Radius of the nucleus, $R_n=1$ fermi $=10^{-15}m$
Volume of the nucleus, $V_n=\frac{4}{3}\pi R_n^3=\frac{4}{3}\times \pi \times {\left(10^{-15}\right)}^3{m}^3$
Their corresponding ratio is
$\frac{V_a}{V_n}=\frac{{\left(10^{-10}\right)}^3}{{\left(10^{-15}\right)}^3}=\frac{10^{-30}}{10^{-45}}=10^{15}$