Question

Density ratio of $O_2$ and $H_2$ is $16:1$. The ratio of their $rms$ velocities will be :

• A. $4:1$
• B. $1:16$
• C. $1:4$
• D. $16:1$

Answer 1

The correct option is C $1:4$

Density ratio of $O_2$ and $H_2$ is $16:1$. The ratio of their RMS velocities will be $1:4$. This is because $rms$ speed is inversely proportional to the square root of density.

$\frac{rm{s}_{O_2}}{rm{s}_{H_2}}=\sqrt{\frac{d_{H_2}}{d_{O_2}}}=\sqrt{\frac{1}{16}}=\frac{1}{4}$

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