Question

The ratio between the root means square velocity of $H_2$ at $50$ K and that of $O_2$ at $800$ K is:

• A. $4$
• B. $2$
• C. $1$
• D. $1/4$

Answer 1

The correct option is C $1$

Root mean square velocity of a gas

$U_{r.m.s}=\sqrt{\frac{3RT}{M}}$

$U_{r.m.s}\left(for{H}_2\right)=\sqrt{\frac{3\times R\times 50}{2}}$

$U_{r.m.s}\left(for{O}_2\right)=\sqrt{\frac{3\times R\times 800}{32}}$

$\frac{U_{r.m.s}\left(for{H}_2\right)}{U_{r.m.s}\left(for{O}_2\right)}=\sqrt{\frac{3\times R\times 50}{2}\times \frac{32}{3\times R\times 800}}=1$

Hence, the correct option is $\text{C}$