Question

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

• A. 4
• B. 2
• C. 1
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

1

Answer 2

The correct answer is C:1
Expression of rms is, $u_{rms}=\sqrt{\frac{3RT}{M}}$
$\Rightarrow \, \, \, \, \frac{u_{rms}(H_2\, at\, 50\, K)}{u_{rms}(O_2\, at\, 800\, K)}=\frac{\sqrt{\frac{3R\times50}{2}}}{\sqrt{\frac{3R\times800}{32}}}$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \sqrt{\frac{50}{2}\times\frac{32}{800}}=1$