One mole of a ideal gas …

Radius of one single hydrogen atom, r = 0.5 {tex}\mathop A\limits^0{/tex} = {tex}0.5 \times 10 ^ { - 10 }{/tex} m (1 {tex}\mathop A\limits^0{/tex} = 10^-10 m)
Volume of one single hydrogen atom {tex}= \frac { 4 } { 3 } \pi r ^ { 3 }{/tex}
{tex}= \frac { 4 } { 3 } \times \frac { 22 } { 7 } \times \left( 0.5 \times 10 ^ { - 10 } \right) ^ { 3 }{/tex}
{tex}= 0.524 \times 10 ^ { - 30 } { m } ^ { 3 }{/tex}
Now, 1 mole of hydrogen atoms means {tex}6.023 \times 10 ^ { 23 }{/tex}  number of hydrogen atoms.(according to Avogadro's hypothesis)
{tex}\therefore{/tex} Atomic volume of 1 mole of hydrogen atoms, {tex}V _ { H _ { 2 } }{/tex} = Avogadro's number {tex}\times{/tex} volume of one single hydrogen atom {tex}= 6.023 \times 10 ^ { 23 } \times 0.524 \times 10 ^ { - 30 } \mathrm { m } ^ { 3 }{/tex}
{tex}= 3.16 \times 10 ^ { - 7 } { m } ^ { 3 }{/tex}
Molar volume of 1 mole of hydrogen atoms at STP,
{tex} { V } _ { m } = 22.4 L = 22.4 \times 10 ^ { - 3 } { m } ^ { 3 }{/tex} (1 litre = 10^-3 m³)

Now, ratio of molar volume of 22.4 L of H₂ to the atomic volume of 1 mole of H₂,
{tex}\therefore \frac { V _ { m } } { V _ { H_2 } } = \frac { 22.4 \times 10 ^ { - 3 } } { 3.16 \times 10 ^ { - 7 } } = 7.08 \times 10 ^ { 4 }{/tex}
Hence, the molar volume is {tex}7.08 \times 10 ^ { 4 }{/tex} times higher than the atomic volume. For this reason, the inter-atomic separation in hydrogen gas is much larger than the size of a hydrogen atom.