The ratio among most probable velocity, mean velocity and root mean square velocity is given by:(a) 1: 2: 3(b) 1: √2: √3(c) √2: √3: √8/π(d) √2: √8/π: √3

Most probable velocity,

\(U_{RMS}=\sqrt{\frac{3RT}{M}}\)

Average velocity,

\(U_{avg}=\sqrt{\frac{8RT}{\pi M}}\)

Root Mean Square velocity,

\(U_{MP}= \sqrt{\frac{2RT}{M}}\)

Therefore,

\(U_{MP}: U_{avg}: U_{RMS}\\\Rightarrow \sqrt{2}:\sqrt{\frac{8}{\pi }}:\sqrt{3}\)

Hence, the correct option is (d) 

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