The density of hydrogen gas at STP is $0.09 \mathrm{kg} {\mathrm{m}}^{-3}$. The mean kinetic energy of one gram molecule of hydrogen gas is approx [UP CPMT 2015]

Given, $\rho = 0.09 \mathrm{kg} {\mathrm{m}}^{-3}$

Pressure, p (at STP) $1.01 \times {10}^5 Pa$
According to kinetic theory of gas,
               $p = (1/3)\rho v^2$

$\Rightarrow$          $v=\sqrt{\frac{3p}{\rho }}=\sqrt{\frac{3\times 1.01\times {10}^5}{0.09}}$

                 $= 1834.85 m{s}^{-1}$

Now, volume occupied by one mole of hydrogen at STP

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

$\therefore$     Mass of hydrogen = Volume $\times$ Density
                                 $$\begin{gathered} = 22.4 \times {10}^{-3} \times 0.09 \\ = 2.016 \times {10}^{-3} kg \end{gathered}$$

$\therefore$  Average kinetic energy per mol $=\frac{1}{2}m{v}^2$

                                $=\frac{1}{2}\times 2.016\times {10}^{-3}\times (1834.85{)}^2$

                                = 3403 J