Question

An ideal diatomic gas at 300 K has molecules of moment of intertia 8.28 x 10^-38 g cm² . The root mean square angular velocity of the molecules in radian per second is

(1) 1 x 10¹² 

(2) 1/√2 x 10¹²

(3) √3 x 10¹²

(4) √4 x 10¹²

Answer 1

(1) 1 x 10¹² 

Rotational kinetic energy = 1/2 Iω² ....(1)

where ω is root mean square angular speed. There are two degrees of freedom of rotational motion i.e. clockwise or anticlockwise. Using Boltzmann’s law of equipartition of energy

From Eqns. (1) and (2) we have