Step 1: Understanding kinetic theory.
The kinetic theory of gases states that the average kinetic energy of gas molecules depends only on the temperature of the gas, regardless of the type of molecule. This means that for a diatomic molecule, its average energy depends only on temperature.
Step 2: Analyzing the options.
(A) mass of each atom and the temperature: Incorrect — The average energy depends only on temperature, not on the mass of individual atoms.
(B) mass of each atom and the bond length: Incorrect — These factors do not directly influence the average energy.
(C) mass of each atom, bond length, and temperature: Incorrect — Only temperature affects the average energy.
(D) temperature only: Correct — The average energy of a molecule in an ideal gas depends only on temperature.
Step 3: Conclusion.
The correct answer is (D) temperature only, as the average energy is directly related to temperature.