Answer
$\beta = 6.4\times 10^{-6}$
Work Step by Step
We can find the root mean square speed of a hydrogen molecule at room temperature:
$v = \sqrt{\frac{3RT}{M}}$
$v = \sqrt{\frac{(3)(8.31~J/mol~K)(300~K)}{2.02\times 10^{-3}~kg/mol}}$
$v = 1920~m/s$
We can find the speed parameter $\beta$:
$\beta = \frac{v}{c}$
$\beta = \frac{1920~m/s}{3.0\times 10^8~m/s}$
$\beta = 6.4\times 10^{-6}$
