Continue the development of Problem 12D.12 by using the virial expression to relate 〈x²〉 to the vibrational quantum number. Does your result imply that the rotational constant increases or decreases as the oscillator becomes excited to higher quantum states. What would be the effect of anharmonicity?

Data in Problem 12D.12

Suppose that the internuclear distance may be written R=R_e+x where R_e is the equilibrium bond length. Also suppose that the potential well is symmetrical and confines the oscillator to small displacements. Deduce expressions for 1/〈R〉², 1/〈R²〉, and 〈1/R²〉 to the lowest non-zero power of 〈x₂〉/R_e² and confirm that values are not the same.