The average energy of a diatomic molecule in an ideal gas depends only on temperature, as per the kinetic theory of gases. This makes option (D) correct for the given multiple-choice question. The equipartition theorem assigns energy based on degrees of freedom, independent of molecular mass or structure details like bond length.​

Option Analysis

• (A) Mass of each atom and temperature: Incorrect. Mass affects velocity (v_rms ∝ 1/√m) but not total average energy, which follows E = (f/2) kT where f=5 for diatomic gases at room temperature (3 translational + 2 rotational).​

• (B) Mass of each atom and bond length: Incorrect. Neither mass nor bond length influences average energy; bond length relates to rotational inertia but energy per degree of freedom remains (1/2) kT.​

• (C) Mass, bond length, and temperature: Incorrect. Adds irrelevant factors to temperature, the sole dependency via equipartition.​

• (D) Temperature only: Correct. Total energy E = (5/2) kT per molecule, proportional to T alone.​

Introduction

In kinetic theory of gases, the average energy of a diatomic molecule in an ideal gas hinges on a single factor: temperature. This principle, rooted in the equipartition theorem, explains why options involving mass or bond length fail in competitive exams like CSIR NET. Explore the detailed science behind this dependency.​

Degrees of Freedom Explained

Diatomic molecules like O₂ or N₂ have 5 degrees of freedom at room temperature: 3 translational and 2 rotational. Vibrational modes activate only at higher temperatures. Each contributes (1/2) kT, yielding total average energy (5/2) kT per molecule—directly tied to T.​

Why Mass Doesn’t Matter

Molecular mass influences speed (lighter molecules move faster for same energy) but not total energy allocation. Translational kinetic energy averages (3/2) kT across all ideal gases, regardless of atomic mass.​

Bond Length Irrelevance

Bond length affects moment of inertia for rotation but not energy per mode. Equipartition ensures fixed (1/2) kT per rotational degree, making structure details secondary to temperature.​

Exam Application

For CSIR NET aspirants, recognize E ∝ T for internal energy in ideal gases. This holds for diatomic cases without intermolecular forces or quantum effects altering equipartition.​