The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$, then the ratio of r.m…

The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$, then the ratio of r.m.s. velocities will be:
  1. $\frac{25}{4}$
  2. $\frac{2}{5}$
  3. $\frac{5}{2}$
  4. $\frac{4}{25}$

Solution

(Vapor density) $=\left(\frac{\text { Molar mass }}{2}\right)$, I.e, $v d=\frac{M}{2}$
$\begin{aligned} & v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} \\ & \frac{v_2}{v_1}=\sqrt{\frac{M_1}{M_2}}=\sqrt{\frac{25}{4}}=\frac{5}{2}\end{aligned}$

Asked in: JEE Main 2025 (28 Jan Shift 2)

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