Given that
Molar volume of ideal gas( H_2 ) = 22.4 \text{ litters } = 22.4 m^{3}
Diameter of the hydrogen molecule = 1 \text{ angstrom } (A^{^o})
Radius of hydrogen molecule = 0.5 * 10^{-10} meters
Avogadro constant = 6.023*10^{23}\ mol^{-1}
Step 1: Calculating one mole of hydrogen's atomic volume
Volume of hydrogen atom(Sphere) = \frac{4}{3} \pi r^3
=\frac{4}{3}*3.14*(0.5*10^{-10})^3
= 0.524 * 10^{-30} m^3
1 mole of hydrogen contains 6.023 * 10^{23} hydrogen atoms.
Volume of 1 mole of hydrogen atoms = 6.023 * 10^{23} * 0.524 * 10^{-30}
= 3.16* 10^{-7} m^3
Hence, total volume of mole of hydrogen atoms = 3.16* 10^{-7} m^3
Step 2: Determine the ratio of molar volume to the atomic volume
\frac{\text{ molar volume }}{\text{ atomic volume }}=\frac{22.4*10^{-3}}{3.16*10^{-7}}
\frac{\text{ molar volume }}{\text{ atomic volume }} = 7 * 10^{4}
Hence, \text{ molar volume } = \text{ atomic volume } * 7 * 10^{4}
This high ratio is due to the intermolecular gasses being significantly greater than the molecular size.