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) $\frac{1}{4}$

Show Answer

Solution:

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

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



NCERT Chapter Video Solution

Dual Pane