The rms speed of oxygen at room temperature is about 500 m/s. The rms speed of hydrogen at the same temperature is about

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2000 ms−1 Given, Molecular mass of hydrogen, MH = 2 Molecular mass of oxygen, Mo = 32 RMS speed is given by, v_{rms =} $\sqrt$(3RT/M) \Rightarrow $\sqrt$(3RT/M_O) = 500 Now , \Rightarrow \frac{v_{Orms}}{v_{Hrms}} = $\sqrt$(3RT/M_O)/$\sqrt$(3RT/M_H) \Rightarrow \frac{v_O rms}{v_{Hrms}} = $\sqrt$(3RT/32)/$\sqrt$(3RT/2) \Rightarrow \frac{v_{Orms}}{{v_H}_{rms}} = $\frac{1}{4}$ \Rightarrow \frac{500}{v_{Hrms}} = $\frac{1}{4}$ \Rightarrow v_{Hrms} = 4 $\times$ 500 = 2000 {\text { ms }}^{- 1}

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