Question

Assertion: Each vibrational mode gives two degrees of freedom.
Reason: By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is $2k_{B}T$.

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

Answer 1

The correct option is C Assertion is true but reason is false.

By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is $\frac{1}{2}{k}_{B}T$.
Each quadratic term form in the total energy expression of a molecules is counted as a degree of freedom. Thus each vibriational mode gives 2 degrees of freedom i.e., kinetic and potential energy modes, corresponding to the energy $2\left(\frac{1}{2}{k}_{B}T\right)=k_{B}T$.