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

विकल्प

• 125 m s⁻¹

• 2000 m s⁻¹

• 8000 m s⁻¹

• 31 m s⁻¹.

Answer 1

2000 ms⁻¹

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

\[v_{rms =} \sqrt{\frac{3RT}{M}}\] 

\[   \Rightarrow \sqrt{\frac{3RT}{M_O}} = 500\]

Now ,

\[ \Rightarrow \frac{v_{Orms}}{v_{Hrms}} = \frac{\sqrt{\frac{3RT}{M_O}}}{\sqrt{\frac{3RT}{M_H}}}\] 

\[ \Rightarrow \frac{v_O rms}{v_{Hrms}} = \frac{\sqrt{\frac{3RT}{32}}}{\sqrt{\frac{3RT}{2}}}\] 

\[ \Rightarrow \frac{v_{Orms}}{{v_H}_{rms}} = \frac{1}{4}\] 

\[ \Rightarrow \frac{500}{v_{Hrms}} = \frac{1}{4}\] 

\[ \Rightarrow  v_{Hrms}  = 4 \times 500 = 2000   {\text { ms }}^{- 1} \]