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