Assertion : Vibrational energy of diatomic molecule corresponding...

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 $=2 \times \frac{1}{2} k_B T=k_B T$