The energy of a diatomic molecule with the inclusion of the anharmonicity, rotation-vibration interaction and centrifugal distortion terms gives us

\begin{equation} E_{int}=E_{el}+h\nu_e(v+1/2)-h\nu_e x_e(v+1/2)^2+hB_eJ(J+1)-h\alpha_e (v+1/2)J(J+1)-hDJ^2(J+1)^2 \end{equation}

If we add the translational energy to this internal energy, we obtain the total energy of the molecule $E=E_{tr}+E_{int}$

**True or false?** (a) The spacings between adjacent translational, rotational and vibrational molecular levels satisfy $\Delta\epsilon_{tr}<\Delta\epsilon_{rot}<\Delta\epsilon_{vib}$. (b) At room temperature, many rotational levels of molecules in the gas phase are significantly crowded. (c) At room temperature, many vibrational levels of $O_2(g)$ are significantly crowded. (d) The vibrational levels of a diatomic molecule are precisely given by the expression of the harmonic oscillator $(v+1/2)h\nu$. (e) A bonding electronic state of a diatomic molecule has a finite number of vibrational levels. (f) As the vibrational quantum number increases, the spacing between adjacent vibrational levels of a diatomic molecule decreases. (g) $D_o>D_e$. (h) As the rotational quantum number J increases, the spacing between adjacent rotational levels of a diatomic molecule increases.