The rms velocity of oxygen molecules of $27^{\circ} \mathrm{C}$ is around $800 \mathrm{~m} / \mathrm{s}$.…
The rms velocity of oxygen molecules of $27^{\circ} \mathrm{C}$ is around $800 \mathrm{~m} / \mathrm{s}$. The rms velocity of methane molecule at $600 \mathrm{~K}$ temperature is around ......
$400 \mathrm{~m} / \mathrm{s}$
$1600 \mathrm{~m} / \mathrm{s}$
$800 \mathrm{~m} / \mathrm{s}$
$1200 \mathrm{~m} / \mathrm{s}$
Solution
$v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}$
Let the rms velocity of methane molecule at $600 \mathrm{~K}$ be $x$.
$
\begin{aligned}
\frac{v_{\mathrm{mss}}\left(\mathrm{O}_2\right)}{v_{\mathrm{ms}}\left(\mathrm{CH}_4\right)} & =\frac{800}{\mathrm{x}}=\frac{\frac{\sqrt{3 R(300 \mathrm{~K})}}{32}}{\frac{\sqrt{3 R(600 \mathrm{~K})}}{16}} \\
& =\frac{800}{x}=\sqrt{\frac{300}{32} \times \frac{16}{600}} \\
\Rightarrow \quad \frac{800}{x} & =\frac{1}{2} \\
x & =1600 \mathrm{~m} / \mathrm{s}
\end{aligned}
$
Hence, the correct option is (2)