Solution:
Solution
According to the kinetic theory of gases
$${C}_{rms} = \sqrt{\dfrac{3RT}{M}}$$
at constant temperature
$${C}_{rms} \alpha \sqrt{\dfrac{1}{M}}$$
$$\dfrac{{C}_{rms of {H}_{2}}}{{C}_{rms of {O}_{2}}} = \sqrt{\dfrac{{M}_{{O}_{2}}}{{M}_{{H}_{2}}}}$$ eq(1)
$${M}_{{O}_{2}} = 16 \times {M}_{{H}_{2}}$$
$$\dfrac{{M}_{{O}_{2}}}{{M}_{{H}_{2}}} = 16$$
substitute values back in eq(1)
$$\dfrac{{C}_{rms of {H}_{2}}}{{C}_{rms of {O}_{2}}} = 4$$
$${C}_{rms of {H}_{2}} = 4 \times {C}_{rms}$$