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The $\mathrm{RMS}$ velocity of $\mathrm{CH}_{4}, \mathrm{He}$ and $\mathrm{SO}_{2}$ are in the ratio of
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Verified Answer
The correct answer is:
$2: 4: 1$
$v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}$
$v_{\mathrm{rms}} \propto \frac{1}{\sqrt{M}}$, where $M=$ molecular mass
$$
\begin{aligned}
&\Rightarrow v_{\mathrm{rms}_{\left(\mathrm{CH}_{4}\right)}}: v_{\mathrm{rms}_{(\mathrm{He})}}: v_{\mathrm{rms}_{\left(\mathrm{SO}_{2}\right)}} \\
&\Rightarrow \quad \frac{1}{\sqrt{16}}: \frac{1}{\sqrt{4}}: \frac{1}{\sqrt{64}} \Rightarrow \frac{1}{4}: \frac{1}{2}: \frac{1}{8} \\
&\Rightarrow \quad 2: 4: 1
\end{aligned}
$$
$v_{\mathrm{rms}} \propto \frac{1}{\sqrt{M}}$, where $M=$ molecular mass
$$
\begin{aligned}
&\Rightarrow v_{\mathrm{rms}_{\left(\mathrm{CH}_{4}\right)}}: v_{\mathrm{rms}_{(\mathrm{He})}}: v_{\mathrm{rms}_{\left(\mathrm{SO}_{2}\right)}} \\
&\Rightarrow \quad \frac{1}{\sqrt{16}}: \frac{1}{\sqrt{4}}: \frac{1}{\sqrt{64}} \Rightarrow \frac{1}{4}: \frac{1}{2}: \frac{1}{8} \\
&\Rightarrow \quad 2: 4: 1
\end{aligned}
$$
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