Question

Which one are correct statements, if $u_{rms},u_{MP}$ and $u_{AV}$ are root mean square, most probable and average speed of an ideal monoatomic gas at absolute temperature T, having mass of one molecule m?

• A. No, molecule can have a speed greater than $\sqrt{2}{U}_{rms}$
• B. No, molecule can have a speed less than $u_{MP}/\sqrt{2}$
• C. $u_{MP}<u_{AV}<u_{rms}$
• D. The average kinetic energy of a molecule is $\frac{3}{4}m{u}_{MP}^2$

Answer 1

Answer: (C), (D)

The correct options are
C $u_{MP}<u_{AV}<u_{rms}$
D The average kinetic energy of a molecule is $\frac{3}{4}m{u}_{MP}^2$

$U_{rms}:U_{av}:U_{mp}=\sqrt{\frac{3RT}{M}}:\sqrt{\frac{8RT}{\pi M}}:\sqrt{\frac{2RT}{M}}=\sqrt{3}:\sqrt{\frac{8}{\pi }}:\sqrt{2}=1.2248:1.1284:1$
The average kinetic energy of a molecule is $3/2KT=\frac{3}{4}m{u}_{MP}^2$