Statistical Mechanics · Problem 6.23

Ideal Bose Systems — R. K. Pathria

Physics — Statistical Mechanics · equilibrium-internuclear-distance-rotation

Problem

Show that the fractional change in the equilibrium value of the internuclear distance of a diatomic molecule, as a result of rotation, is given by Δr0r0≃(ℏμr02ω)2J(J+1)=4(ΘrΘv)2J(J+1);\frac{\Delta r_0}{r_0} \simeq \left(\frac{\hbar}{\mu r_0^2 \omega}\right)^2 J(J+1) = 4\left(\frac{\Theta_r}{\Theta_v}\right)^2 J(J+1); here, ω\omega is the angular frequency of the vibrational state in which the molecule happens to be. Estimate the numerical value of this fraction in a typical case.

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