IR Spectroscopy. Wave length ~ 100 m m to 1 m m Wave number ~ 100 to 10,000 cm -1 Frequency ~ 3 x 10 12 to 3 x 10 14 Hz Energy ~ 1 kJ to 100 KJ /mole. HCl absorptions. 2885.9 cm -1 fundamental band strong
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Wave length ~ 100 mm to 1 mm
Wave number ~ 100 to 10,000 cm-1
Frequency ~ 3 x 1012 to 3 x 1014 Hz
Energy ~ 1 kJ to 100 KJ /mole
Centre of mass
does not move!
Transition Moment = Integral
Transition Moment Integral
Must have an oscillating dipole moment
Red – NOT
Change to polar
Variables can be separated!
Up to second order in v and J
Center of mass does not move
Motion is in Phase
All atoms vibrate with same frequency
3N-6 Normal Modes
Bending mode of CO2 - 667 cm-1
We denote normal modes
Symmetric Stretch of CO2 1330 cm-1
Antisymmetric Stretching of CO2, 2349 cm-1
Each Normal Modes = A Hamonic Oscillator
Energy of one hamonic Oscillator is known!
State of the molecule specified by
Selection Rule: Only one of