Question

The rms speed of oxygen at room temperature is about 500 m/s. The rms speed of hydrogen at the same temperature is about
(a) 125 m s⁻¹
(b) 2000 m s⁻¹
(c) 8000 m s⁻¹
(d) 31 m s⁻¹.

Answer 1

(b) 2000 ms⁻¹

Given,
Molecular mass of hydrogen, M_H = 2
Molecular mass of oxygen, M_o = 32
RMS speed is given by,

$$\begin{gathered} v_{rms=}\sqrt{\frac{3RT}{M}} \\ \Rightarrow \sqrt{\frac{\mathit{3}RT}{M_O}}=500 \end{gathered}$$
Now,
$$\begin{gathered} \Rightarrow \frac{v_{Orms}}{v_{Hrms}}=\frac{\sqrt{{\displaystyle \frac{3RT}{M_O}}}}{\sqrt{{\displaystyle \frac{3RT}{M_H}}}} \\ \Rightarrow \frac{v_{O}rms}{v_{Hrms}}=\frac{\sqrt{{\displaystyle \frac{3RT}{32}}}}{\sqrt{{\displaystyle \frac{3RT}{2}}}} \\ \Rightarrow \frac{v_{Orms}}{{v_H}_{rms}}=\frac{1}{4} \\ \Rightarrow \frac{500}{v_{Hrms}}=\frac{1}{4} \\ \Rightarrow v_{Hrms}=4\times 500=2000{\mathrm{ms}}^{-1} \end{gathered}$$

Hence, the correct answer is (b).