Question

The diameter of an atom is $1.2\times {10}^{-10}\mathrm{m}$and the diameter of its nucleus is$1.0\times {10}^{-14}\mathrm{m}$. What percent of the atom's volume is occupied by mass and what percent is empty space?

Short answer

The volume occupied by mass$5.79\times {10}^{-11}\%$

Step-by-step solution

Given information

The diameter of an atom is $1.2\times {10}^{-10}\mathrm{m}$

The diameter of its nucleus is$1.0\times {10}^{-14}\mathrm{m}$.

calculation

All masses are confined in the nucleus. So the ratio will be the ratio nucleus to atoms volume . The volume of the atom is $V_a=\frac{4}{3}\pi r_a^3=\frac{4}{3}\pi {\left(1.2\times {10}^{-10}\right)}^3=7.24\times {10}^{-30}{\mathrm{m}}^3$

The volume of nucleus is$V_n=\frac{4}{3}\pi r_n^3=\frac{4}{3}\pi {\left(1.0\times {10}^{-14}\right)}^3=4.19\times {10}^{-42}{\mathrm{m}}^3$

So the ratio is

$\frac{4.19\times {10}^{-42}}{7.24\times {10}^{-30}}=5.79\times {10}^{-13}=5.79\times {10}^{-11}\%$

So only $5.79\times {10}^{-11\%}$of volume actually occupied by mass