A diatomic gas consisting of rigid molecules is at a temperature of 87^ C . If the moment of inertia of the rotating diatomic rigid molecule is 2.76 10⁻³⁹ gcm ^2 , then the rms angular speed of the molecule is (Boltzmann constant =1.38 10⁻²³ JK ⁻¹ )

Step-by-step solution

Moment of inertia of diatomic molecule, I= 2 3 M r^2 rms speed of molecule, v= 3 k T M rms angular speed, aligned = v r & = 3 k T / M 3 I / 2 M = 2 k T I & = 2 1.38 10⁻²³ (87+273) 2.76 10⁻⁴⁶ & = 360 10²³ = 36 10²⁴ & =6 10¹² rad / s aligned