thermodynamics - Why doesn't hydrogen gas exist in Earth's atmosphere?

The root mean square velocity of hydrogen gas at room temperature is:
Gas constant: $R=8.31\ \mathrm{J\ K^{-1}\ mol^{-1}}$
Molar mass of hydrogen gas: $M=2.02\times10^{-3}\ \mathrm{kg/mol}$
$$\begin{align} v &= \left(\frac{3\times8.31\ \mathrm{J\ K^{-1}\ mol^{-1}}\times300}{2.02\times10^{-3}\ \mathrm{kg/mol}}\right)^{\frac12}\\ &= 3356.8377\ \mathrm{m/s}\\ &= 3.356\ \mathrm{km/s} \end{align}$$
The escape speed of Earth is $11.2\ \mathrm{km/s}$, which is larger than the root mean square velocity of hydrogen gas. But still, hydrogen gas doesn't exist in Earth's atmosphere. Why? Have I made any mistakes in my calculations?