Question

The rms speed of oxygen at room temperature is about $500\text{m/s}$. The rms speed of hydrogen at the same temperature is about

• A. $125\text{m/s}$
• B. $2000\text{m/s}$
• C. $8000\text{m/s}$
• D. $31\text{m/s}$

Answer 1

The correct option is B $2000\text{m/s}$

Given,
$V_{rms}\left(O_2\right)=500\text{m/s}$
We know that, $V_{rms}=\sqrt{\frac{3RT}{M}}$
$\Rightarrow V_{rms}\propto \frac{1}{\sqrt{M}}$
[Temperature is same ]
So, $\frac{V_{rms,H_2}}{V_{rms,O_2}}=\frac{\sqrt{M_{O_2}}}{\sqrt{M_{H_2}}}=\frac{\sqrt{32}}{\sqrt{2}}$
$\Rightarrow \frac{V_{rms,H_2}}{500}=\sqrt{16}\Rightarrow V_{rms,H_2}=2000\text{m/s}$