A) \[{{V}_{rms}}<{{V}_{av}}<{{V}_{mp}}\]
B) \[{{V}_{rms}}>{{V}_{av}}>{{V}_{mp}}\]
C) \[{{V}_{mp}}<{{V}_{rms}}<{{V}_{av}}\]
D) \[{{V}_{mp}}>{{V}_{rms}}>{{V}_{av}}\]
Correct Answer: B
Solution :
Root mean square speed. The root mean square speed is used to measure the velocity of particles in a gas. It is given by \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}=1.732\sqrt{\frac{RT}{M}}\] ?...(1) where M is molar mass and R is gas constant, T is temperature. Most probable speed \[{{v}_{p}}\], is the speed most likely to be possessed by any molecule in the system. \[{{v}_{av}}=\sqrt{\frac{2RT}{M}}=1.41\sqrt{\frac{RT}{M}}\] ??(2) whereas mean speed is \[{{v}_{mp}}=\sqrt{\frac{8RT}{\pi M}}=1.6\sqrt{\frac{RT}{M}}\] .?..(3) From Eqs. (1), (2) and (3), we conclude that \[{{v}_{rms}}>{{v}_{av}}>{{v}_{mp}}\]
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