Question

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

• A. 0.25
• B. 1
• C. 2
• D. 4

Answer 1

The correct option is B 1

The rms velocity is directly proportional to the square root of temperature and inversely proportional to the square root of molecular weight.
The ratio between the root mean square velocity of $H_2$ at $50K$ and that of $O_2$ at $800K$ is
$\frac{u_{H_2}}{u_{O_2}}=\sqrt{\frac{T_{H_2}}{M_{H_2}}\times \frac{M_{O_2}}{T_{O_2}}}$

$\frac{u_{H_2}}{u_{O_2}}=\sqrt{\frac{50}{2}\times \frac{32}{800}}$

$\frac{u_{H_2}}{u_{O_2}}=1$