The fundamental vibrational transition of the 12C16O in theelectronic ground state from v=0 to v=1 occurs at 2,170 cm-1. Thebottom of the Morse potential for the anharmonic oscillator is wellapproximated by a parabola, the potential well for the harmonicoscillator, especially when the transition is measured withprecision limited to 1 cm-1. a) Demonstrate that, in the harmonicoscillator approximation of the IR spectroscopy, the frequency ofthe fundamental transition is equal to the frequency of theoscillator in the zero energy state. b) What is the elastic forceconstant k of the 12C16O bond in the harmonic oscillatorapproximation? (Hint: you have to use the reduced mass of thediatomic oscillator. A12C = 12.000 amu, A16O = 15.995 amu, 1 amu =1.6605 x 10-27 kg, c = 2.9979x108 m s-1) c) The first overtone ofthe 12C16O occurs at 4,260 cm-1. Compare this frequency against thefundamental frequency and state 2 points of departure from theharmonic oscillator results predicted by Quantum Mechanics.
