Question

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

• A. C* : $\overline{C}$ : C = 1.225 : 1.128 : 1
• B. C* : $\overline{C}$ : C = 1.128 : 1.225 : 1
• C. C* : $\overline{C}$ : C = 1 : 1.128 : 1.225
• D. C* : $\overline{C}$ : C = 1 : 1.225 : 1.128

Answer 1

The correct option is C C* : $\overline{C}$ : C = 1 : 1.128 : 1.225

C* = Most probable speed = $\sqrt{\frac{2RT}{M}}$ ...(i)
$\overline{C}$ = Average speed = $\sqrt{\frac{8RT}{\pi M}}$ ...(ii)
C = Root means square speed = $\sqrt{\frac{3RT}{M}}$ ...(iii)
From (i), (ii) and (iii)
$C\ast <\overline{C}<C$