JEE Main 2023 — Kinetic Theory of Gases Question with Solution

The formula to calculate the rms speed of the argon molecules is given by

$v_{Ar}=\sqrt{\frac{3RT}{M_{Ar}}} ...\left(1\right)$

The formula to calculate the rms speed of chlorine molecule is given by

$v_{Cl}=\sqrt{\frac{3RT}{M_{Cl}}} ...\left(2\right)$

Divide equation (1) by equation (2) and simplify to obtain the required ratio.

$\frac{v_{\mathrm{Ar}}}{v_{\mathrm{Cl}}}=\sqrt{\frac{M_{\mathrm{Cl}}}{M_{\mathrm{Ar}}}} ...\left(3\right)$

Substitute the values of the known parameters into equation (3) and solve to calculate the required value.

$\begin{array}{rcl}\frac{v_{\mathrm{Ar}}}{490 \mathrm{m} {\mathrm{s}}^{-1}}& =& \sqrt{\frac{71}{40}}\\ & \Rightarrow & v_{Ar}= \sqrt{\frac{71}{40}}\times 490 \mathrm{m} {\mathrm{s}}^{-1}\\ & \approx & 651.7 \mathrm{m} {\mathrm{s}}^{-1}\end{array}$