Rotational Spectroscopy

Rotational Spectroscopy

1. Rigid Rotor

   • Moment of Inertia: I=(mu)r^2
   • Angular momentum, J=Iw
   • Rotational kinetic energy, E=(J^2)/(2I)= (1/2)Iw^2
   • Energy of diatomic rotation: E= BJ(J+1), where B= (h(bar)^2)/2I
   • Selection rules
     • Gross selection rule: The molecule must possess a permanent dipole
     • Specific selection rule: Change in J= +/-1
   • Transitions seen at 2B(J+1)
     • Lines spaced by 2B
   • Degeneracy of 2J+1 in the absence of external fields
   • Most populated level (population only), Jmax=(kT/2B)^1/2 -1/2

2. Non-rigid rotor

3. General

   • Rotations occur around 10 cm- 1 mm (microwave region)
   • Relative population is given by Boltzmanns law: gi/g0 exp(change in energy/kT)
   • Rate of spontaneous emission is proportional to v^3