Statement I: Each vibrational mode gives two degrees of freedom Statement II: By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is 2kB T.

Question

Statement I: Each vibrational mode gives two degrees of freedom Statement II: By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is 2kB T. (A) Both statement I and II are correct. (B) Both statement I and II are incorrect. (C) Statement I is correct but statement II is incorrect. (D) Statement II is correct but statement I is incorrect.

Tardigrade Admin · Accepted Answer

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 to be counted as a degree of freedom. Thus each vibrational mode gives

2

degree of freedom
i.e, kinetic and potential energy modes, corresponding to the energy

2 (\frac{1}{2} k_{B} T) = k_{B} T

Q. Statement I : Each vibrational mode gives two degrees of freedom Statement II : By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is 2kB​T.

Both statement I and II are correct.

Both statement I and II are incorrect.

Statement I is correct but statement II is incorrect.

Statement II is correct but statement I is incorrect.

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