JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
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:
- A \(\frac{25}{4}\)
- B \(\frac{2}{5}\)
- C \(\frac{5}{2}\)
- D \(\frac{4}{25}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
(Vapor density) \(=\left(\frac{\text { Molar mass }}{2}\right)\), I.e, \(v d=\frac{M}{2}\) \(\begin{aligned} & v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} \\ & \frac{v_2}{v_1}=\sqrt{\frac{M_1}{M_2}}=\sqrt{\frac{25}{4}}=\frac{5}{2}\end{aligned}\)
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