The fundamental vibrational transition of the 12C16O in the electronic ground state from v=0 to v=1...

The fundamental vibrational transition of the 12C16O in the electronic ground state from v=0 to v=1 occurs at 2,170 cm-1. The bottom of the Morse potential for the anharmonic oscillator is well approximated by a parabola, the potential well for the harmonic oscillator, especially when the transition is measured with precision limited to 1 cm-1. a) Demonstrate that, in the harmonic oscillator approximation of the IR spectroscopy, the frequency of the fundamental transition is equal to the frequency of the oscillator in the zero energy state. b) What is the elastic force constant k of the 12C16O bond in the harmonic oscillator approximation? (Hint: you have to use the reduced mass of the diatomic 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 of the 12C16O occurs at 4,260 cm-1. Compare this frequency against the fundamental frequency and state 2 points of departure from the harmonic oscillator results predicted by Quantum Mechanics.

Expert Solution

queen_honey_blossom answered 1 year ago

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