1) The vibrations of an Oxygen molecule, O2 are equivalent to those of harmonic oscillator with a force constant kr= 2294 N/m. Use m("O) = 15.9994 mu, m= 1.66054x102" kg a) Calculate the angular frequency of harmonic oscillator, o. b) Calculate the energies of the states at v-1 and v-2 for the vibration of the oxygen molecule. Find the energy difference between these two states.
1) The vibrations of an Oxygen molecule, O2 are equivalent to those of harmonic oscillator with a force constant kr= 2294 N/m. Use m("O) = 15.9994 mu, m= 1.66054x102" kg a) Calculate the angular frequency of harmonic oscillator, o. b) Calculate the energies of the states at v-1 and v-2 for the vibration of the oxygen molecule. Find the energy difference between these two states.
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Transcribed Image Text:1) The vibrations of an Oxygen molecule, O2 are equivalent to those of harmonic oscillator with a
force constant k= 2294 N/m. Use m(°O) = 15.9994 mụ, m= 1.66054x102' kg
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a) Calculate the angular frequency of harmonic oscillator, o.
b) Calculate the energies of the states at v=1 and v=2 for the vibration of the oxygen molecule.
Find the energy difference between these two states.
c) Find harmonic wavefunction equations for v=1 as a function of y by defining the
normalization constant, N9 and the Hermite polynomial, H9.
d) Wave function and probability density function are plotted in Fig. Q1. Explain the wave and
probability density functions on the figure. What is the number of nodes of this vibrational
motion? Indicate the position of the node on the figure. What is the frequency level
(harmonic) for this plot?
-4
-2
2
4
-4
-2
2
4
Displacement, y3Dx/ a
Displacement, y=x/ a
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