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Last updated date: 08th Dec 2023
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# Assertion: Vibrational energy of a diatomic molecule corresponding to each degree of freedom is ${k_B}T$ .Reason: For every molecule, the vibrational degree of freedom is 2.(a) Both assertion and reason are correct and the reason is the correct explanation for assertion.(b) Both assertion and reason are correct but the reason is not the correct explanation of assertion.(c) Assertion is correct but the reason is incorrect(d) Both assertion and reason are incorrect

According to law of equipartition of energy, in thermal equilibrium, at temperature $T$ , each degree of freedom of transitional, rotational and vibrational motion contributes an average energy equal to $\dfrac{1}{2}{k_B}T$ . The vibrational motion has two types of energy associated with the vibrations along the length of the molecule-kinetic energy and potential energy. Thus, it contributes two degrees of freedom. Thus vibrational energy $= 2 \times \dfrac{1}{2}{k_B}T = {k_B}T$ .