Question

Calculate the ratio of $rms$ speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature.

• A. $1 : 4$
• B. $1 : 8$
• C. $1 : 2$
• D. $1 : 6$

Answer 1

Answer: (A)

$1 : 4$

Answer 2

Root mean square velocity
$V_{rms} \propto\frac{1}{\sqrt{M}}$
so $\frac{\left(V_{rms}\right)O_{2}}{\left(V_{rms}\right)H_{2}}=\sqrt{\frac{M_{H_2}}{M_{O_2}}}$
$=\sqrt{\frac{2}{32}}=\frac{1}{4}$