Question

A mixture of two gases is contained in a vessel. The gas $1$ is monoatomic and gas $2$ is diatomic and the ratio of their molecular masses $M_1/M_2=1/4$. What is the ratio of root mean square speeds of the molecules of two gases?

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is A $2$

From kinetic theory of gases
$p=\frac{1}{3}\frac{M}{V}\cdot e^2$
Since, $p$ and $V$ are constant (same)
$\therefore M_1{e}_1^2=M_2{e}_2^2$
$\Rightarrow \frac{e_1^2}{e_2^2}=\frac{M_2}{M_1}$
$\Rightarrow \frac{e_1}{e_2}=\sqrt{\frac{M_2}{M_1}}=\sqrt{4/1}=2[given,\frac{M_1}{M_2}=\frac{1}{4}]$.