Transitions between energy levels in atoms or molecules depend upon the satisfaction of selection rules. The...

    

Transcribed Image Text:

Transitions between energy levels in atoms or molecules depend upon the satisfaction of selection rules. The strength for a transition from an initial state with wavefunction b; to a final state with wavefunction bf is given by the transition moment integral: Ix where û. is the transition moment operator. For rotational and vibrational spectroscopy the dipole moment plays a critical role in this operator. The dipole moment can be expanded about the value at the equilibrium internuclear distance: ), dQ+... Qe u = le + aQ where dQ is the change in the geometry of the molecule. For a molecule to have a rotational absorption spectrum the permanent dipole moment must be non-zero and for a molecule to have a vibrational absorption spectrum the change in dipole moment with changing geometry must be non-zero. Vibrational modes are Raman allowed if there is a change in polarizability with changing molecular geometry: da a = ao+ Because this leads to an induced dipole in the molecule: Min = aE Part C For the set of molecules listed below, indicate if they have a Raman spectrum. Nitrogen gas (N2) Carbon Monoxide Gas (CO) Carbon Tetrachloride (CCl4) Carbon Dioxide (CO2) Boron Triflouride (BF3) Water (H2O) Transitions between energy levels in atoms or molecules depend upon the satisfaction of selection rules. The strength for a transition from an initial state with wavefunction b; to a final state with wavefunction bf is given by the transition moment integral: Ix where û. is the transition moment operator. For rotational and vibrational spectroscopy the dipole moment plays a critical role in this operator. The dipole moment can be expanded about the value at the equilibrium internuclear distance: ), dQ+... Qe u = le + aQ where dQ is the change in the geometry of the molecule. For a molecule to have a rotational absorption spectrum the permanent dipole moment must be non-zero and for a molecule to have a vibrational absorption spectrum the change in dipole moment with changing geometry must be non-zero. Vibrational modes are Raman allowed if there is a change in polarizability with changing molecular geometry: da a = ao+ Because this leads to an induced dipole in the molecule: Min = aE Part C For the set of molecules listed below, indicate if they have a Raman spectrum. Nitrogen gas (N2) Carbon Monoxide Gas (CO) Carbon Tetrachloride (CCl4) Carbon Dioxide (CO2) Boron Triflouride (BF3) Water (H2O)