question_answer 25)

                  In a diatomic molecule, the rotational energy at a given temperature                 (a) obeys Maxwell s distribution.                 (b) have die same value for all molecules.                 (c) equals the translational kinetic energy for each molecule.                 (a) is (2/3)rd the translational kinetic energy for each molecule.

Answer:

                  (a, d)                 (a) \[{{E}_{t}}\] and \[{{E}_{r}}\] both obey Maxwell?s distribution independent of each other.                 (d) Kinetic energy of translation/molecule, \[{{E}_{t}}=3\left( \frac{1}{2}{{k}_{B}}T \right)=\frac{3}{2}{{k}_{B}}T\]                 Kinetic energy of rotation/molecule, \[{{E}_{r}}=2\left( \frac{1}{2}{{k}_{B}}T \right)={{k}_{B}}T\]                 Clearly,  \[{{E}_{r}}=\frac{2}{3}{{E}_{t}}\]