Question

Assertion : Vibrational energy of diatomic molecule corresponding to each degree of freedom is k_BT.
Reason : For every molecule, vibrational degree of freedom is 2.

• A. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (C)

According to law of equipartition of energy, in thermal equilibrium, at temperature T, each degree of freedom of translational, rotational and vibrational motion contributes an average energy equal to $\frac{1}{2}k_{B}T$. 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 $=2\times\frac{1}{2}k_{B}T=k_{B}T.$