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) $\dfrac{1}{4}$

Show Answer

Answer:

Correct Answer: 26. (c)

Solution:

Expression of $rms$ is, $u _{rms}=\sqrt{\dfrac{3 R T}{M}}$

$ \begin{aligned} \Rightarrow \quad \dfrac{u _{rms}\left(H _2 \text { at } 50 K\right)}{u _{rms}\left(O _2 \text { at } 800 K\right)} & =\dfrac{\sqrt{\dfrac{3 R \times 50}{2}}}{\sqrt{\dfrac{3 R \times 800}{32}}} \\ & =\sqrt{\dfrac{50}{2} \times \dfrac{32}{800}}=1 \end{aligned} $

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