Question

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

Answer 1

Hint: In order to answer this question, check whether the given reason is correct for the given assertion or not, so as we know the given statement is related with the law of equipartition of energy. So we will go through the concept of the law of equipartition of energy.

Complete step by step answer:
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$ .
The law of equipartition, energy equipartition, and simply equipartition are all names for the equipartition theorem. The original concept of equipartition was that in thermal equilibrium, energy is distributed evenly among all of its forms; for example, the average kinetic energy per degree of freedom in a molecule's translational motion should be equal to that in rotational motion.
For each mode of energy (translational, vibrational, and rotational), the amount of energies contained inside the molecule is employed. Gases' Degree of Freedom Consider an atom's solitary particle, which is free to wander about in three dimensions.
Hence, the given reason is the correct explanation for the given assertion.

Note: Now a question arises here about how Equipartition works? So, a particle requires energy to travel, which is generated by the energy stored in an atom. For each mode of energy (translational, vibrational, and rotational), the Law of Equipartition of Energy is utilised to describe the amount of energies held inside the molecule.