AP EAMCET · PHYSICS · Kinetic Theory of Gases

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 $2.76 \times 10^{- 39} {gcm}^{2}$ then the rms angular speed of the molecule is $($ Boltzmann constant $= 1.38 \times 10^{- 23} {JK}^{- 1}$ )

A $6 \times 10^{12} {rads}^{- 1}$
B $3 \times 10^{12} {rads}^{- 1}$
C $6 \times 10^{13} {rads}^{- 1}$
D $3 \times 10^{13} {rads}^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(A) $6 \times 10^{12} {rads}^{- 1}$

Step-by-step Solution

Detailed explanation

Recall the formula of the kinetic energy of one molecule in terms of Boltzmann constant and absolute temperature, K.E.=12KT, for two rigid molecules, it will be, K.E.=2×12KT=KT, if I is a moment of inertia of body and ω is the angular velocity then,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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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 2.76×10-39gcm2 then the rms angular speed of the molecule is (Boltzmann constant =1.38×10-23JK-1)

Step-by-step Solution

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 $2.76 \times 10^{- 39} {gcm}^{2}$ then the rms angular speed of the molecule is $($ Boltzmann constant $= 1.38 \times 10^{- 23} {JK}^{- 1}$ )