One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). The ratio of molar volume to the atomic volume of a mole of hydrogen? (Take the size of hydrogen molecule to be about  $1\stackrel{0}{A}$)

Given, molar volume of one mole of hydrogen

$=22.4L=22.4\times {10}^{-3}{m}^3$

Diameter of hydrogen molecule (d) $=1\stackrel{0}{A}={10}^{-10}m$

$\therefore$ Radius of hydrogen molecule (r) $=\frac{d}{2}=\frac{{10}^{-10}}{2}=0.5\times {10}^{-10}m$

Volume of one molecule of hydrogen $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times 3.14\times {(0.5\times {10}^{-10})}^3$

$=5.234\times {10}^{-31}{m}^3$

Number of molecules in one mole of hydrogen = Avogadro number (N)

$=6.023\times {10}^{23}$

$\therefore$Atomic volume of one mole of hydrogen

= Number of molecules in one mole of hydrogen $\times$ Volume of one molecule of hydrogen

$6.023\times {10}^{23}\times 5.234\times {10}^{-31}$

$=31.52\times {10}^{-7}{m}^3$

Now, $\frac{Molarvolume}{Atomicvolume}=\frac{22.4\times {10}^{-3}}{3.154\times {10}^{-7}}=7.1\times {10}^4$