## Chemistry: Molecular Approach (4th Edition)

$\underline{6.8\times {{10}^{-15}}}$
Radius of hydrogen atom is $52.9\text{ pm}$. $\text{1 pm}=\text{1}{{\text{0}}^{-10}}\text{ cm}$ Thus, radius of hydrogen atom in centimeters is written as follows: $r=52.9\times {{10}^{-10}}\text{ cm}$ Now, volume of an atom (sphere) is as follows: $V=\frac{4}{3}\pi {{r}^{3}}$ Thus, $V=\frac{4}{3}\pi {{\left( 52.9\times {{10}^{-10}}\text{ cm} \right)}^{3}}$ Radius of proton is $1.0\times {{10}^{-13}}cm$. Thus, volume of a proton is as follows: $V=\frac{4}{3}\pi {{\left( 1.0\times {{10}^{-13}}\ \text{cm} \right)}^{3}}$ Now, fraction of the space within the atom occupied by the nucleus is as follows: \begin{align} & F=\frac{\frac{4}{3}\pi {{\left( 1.0\times {{10}^{-13}}\ \text{cm} \right)}^{3}}}{\frac{4}{3}\pi {{\left( 52.9\times {{10}^{-10}}\text{ cm} \right)}^{3}}} \\ & =6.8\times {{10}^{-15}} \end{align} The fraction of the space within the atom occupied by the nucleus is $\underline{6.8\times {{10}^{-15}}}$.