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If I is the moment of inertia of a rigid diatomic molecule, then calculate the angular mean square velocity of a rotating molecule in the gas sample, if the temperature is T. (k = Boltzmann constant)

a
2kTI
b
kTI
c
3kTI
d
5kTI

detailed solution

Correct option is A

Given, Diatomic gas is at temperature T. Rotational kinetic energy = 2 ×kT2 Because diatomic gas has two degrees of rotationRotational Kinetic energyKErot=12Iω2⇒12Iω2=2kT2⇒12Iω2=kT⇒Iω2=2kT⇒ω2=2kTI∴ω=2kTI

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