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)

${10}^{15}$

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