Q31
General SciencePhysics
Ratio of the rms speed and the most probable speed for molecules in an ideal gas is
- a.$\sqrt{3} : 1$
- b.$1 : \sqrt{3}$
- c.$\sqrt{3} : \sqrt{2}$
- d.$\sqrt{2} : \sqrt{3}$
Answer: (C) $\sqrt{3} : \sqrt{2}$
For an ideal gas, $v_{rms}=\sqrt{\frac{3RT}{M}}$, average speed $v_{avg}=\sqrt{\frac{8RT}{\pi M}}$ and most probable speed $v_{mp}=\sqrt{\frac{2RT}{M}}$. Hence $v_{rms}:v_{mp}=\sqrt{3}:\sqrt{2}\approx1.22:1$. Option (D) is the inverse ratio ($v_{mp}:v_{rms}$). Remember the order $v_{mp}<v_{avg}<v_{rms}$, in the ratio $1:1.128:1.224$; all three rise with temperature and fall with increasing molar mass.