Question

The rms speed of oxygen at room temperature is about $500m{s}^{-1}.$ The rms speed of hydrogen at the same temperature is about

• A. $125m{s}^{-1}$
• B. $2000m{s}^{-1}$
• C. $8000m{s}^{-1}$
• D. $31m{s}^{-1}$

Answer 1

Answer: (B)

RMS speed of gas is given by
$v_{rms}=\sqrt{\frac{3RT}{M}}$
Where, $R=$ gas constant
$T=$ absolute temperature in Kelvin
$M=$ molecular mass of the gas
$\therefore \frac{\left(V_{rms}\right)oxygen}{\left(V_{rms}\right)hydrogen}=\sqrt{\frac{M_{H_2}}{M_{O_2}}}=\sqrt{\frac{2}{32}}$
$=\sqrt{\frac{1}{16}}=\frac{1}{4}$
$\Rightarrow \frac{500}{(V_{rms})hydrogen}=\frac{1}{4}$
$\Rightarrow \left(V_{rms}\right)$ hydrogen $=2000m{s}^{-1}$