The harmonic oscillator, rigid-rotor wavefunctions are usually pretty accurate a

Question

The harmonic oscillator, rigid-rotor wavefunctions are usually pretty accurate approximations for the wavefunctions of a diatomic molecule lying low within a potential well, even though the energies may be better represented by that for an anharmonic, rigid rotor. What would the harmonic oscillator, rigid rotor wavefunctions be for 14N16O if it were treated in this manner when in a state with an energy of 8294.111 cm-1 ? Give at least 3 possibilities. The vibrational constants for 14N16O are e = 1904.20 cm-1 and ee = 14.075 cm-1 . The rigid rotor equilibrium bondlength is 1.15077 Å.

Explanation / Answer

According to the given data:

The frequecy for fundamental transition

v0-1 = e - 2ee

The frequency for first overtone

v0-2 = 2e - 6ee

The frequency for second overtone

v0-3 = 3e - 12ee

Now, one of the transitions have the frequency of 8294.111 cm-1.

Here, e = 1904.20 cm-1 and ee = 14.075 cm-1

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