Q1(d). Equipartition in hydrogen

Answer in brief

The classical mean thermal energy is 7/2 k_BT per molecule, or 7/2RT per mole.

Key points

• Each independent quadratic term in the energy contributes 1/2 k_BT to the mean energy at thermal equilibrium.
• A linear diatomic molecule has three translational and two rotational quadratic terms. Its one vibrational mode has both kinetic and potential terms, contributing k_BT.
• Therefore ⟨ E⟩=(3/2+2/2+1)k_BT=7k_BT/2. This is the classical fully excited translation–rotation–vibration limit; electronic excitation and the choice of zero-point reference are not included.