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 )

Question

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 ), 6 × 10 12 rads - 1, 3 × 10 12 rads - 1, 6 × 10 13 rads - 1, 3 × 10 13 rads - 1

MARKS App · Accepted Answer

Recall the formula of the kinetic energy of one molecule in terms of Boltzmann constant and absolute temperature, K . E . = 1 2 K T , for two rigid molecules, it will be, K . E . = 2 × 1 2 K T = K T , if I is a moment of inertia of body and ω is the angular velocity then, K T = 1 2 I ω 2 ⇒ ω = 2 K T I = 2 × 1 . 38 × 10 - 23 87 + 273 2 . 76 × 10 - 39 × 10 - 7 = 6 × 10 12 rad s - 1

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