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Question: For gaseous state, if most probable speed is denoted by C\*, average speed by and mean square speed ...

For gaseous state, if most probable speed is denoted by C*, average speed by and mean square speed by C, then for a large number of molecules the ratios of these speeds are :

A

C* : : C = 1.225 : 1.128 : 1

B

C* : : C = 1.128 : 1.225 : 1

C

C* : : C = 1 : 1.128 : 1.225

D

C* : : C = 1 : 1.225 : 1.128

Answer

C* : : C = 1 : 1.128 : 1.225

Explanation

Solution

C* = most probable speed =2RTM= \sqrt{\frac{2RT}{M}}

Cˉ\bar{C}= average speed=8RTπM= \sqrt{\frac{8RT}{\pi M}}

C = Mean square speed corrected as rms=3RTM= \sqrt{\frac{3RT}{M}}

C* <Cˉ\bar{C}<C

C* : Cˉ\bar{C} : C = 1 :4π\sqrt{\frac{4}{\pi}} : 32\sqrt{\frac{3}{2}}= 1 : 1.128 : 1.225

Note : As no option correspond to mean square speed, it is understood as misprint. It should be root means square speed

So, Ans is (3)