States of Matter - Result Question 26
####26. The ratio between the root mean square speed of $H _2$ at $50 K$ and that of $O _2$ at $800 K$ is
(1996, 1M)
(a) 4
(b) 2
(c) 1
(d) $\frac{1}{4}$
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Solution:
- Expression of $rms$ is, $u _{rms}=\sqrt{\frac{3 R T}{M}}$
$$ \begin{aligned} \Rightarrow \quad \frac{u _{rms}\left(H _2 \text { at } 50 K\right)}{u _{rms}\left(O _2 \text { at } 800 K\right)} & =\frac{\sqrt{\frac{3 R \times 50}{2}}}{\sqrt{\frac{3 R \times 800}{32}}} \ & =\sqrt{\frac{50}{2} \times \frac{32}{800}}=1 \end{aligned} $$
