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  4. The ratio between the root mean square speed of H2 at 50 K and that of O2 at 800 K is

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Q. The ratio between the root mean square speed of $H_2$ at $50\, K$ and that of $O_2$ at $800 \,K$ is

IIT JEEIIT JEE 1996States of Matter

Solution:

Expression of rms is, $u_{ rms }=\sqrt{\frac{3 R T}{M}}$
$\Rightarrow \frac{u_{ rms }\left( H _{2} \text { at } 50 K \right)}{u_{ rms }\left( O _{2} \text { at } 800 K \right)}=\frac{\sqrt{\frac{3 R \times 50}{2}}}{\sqrt{\frac{3 R \times 800}{32}}}$
$=\sqrt{\frac{50}{2} \times \frac{32}{800}}=1$