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18 Nov 2019
Consider a diatomic molecule such as HCl. The fundamental vibrational frequency has been measured as v 2991 cm-1. The dissociation energy is De 7.31 x 10-19 J. De is the energy difference between the minimum of the potential well and the separated atoms. Therefore, the lowest vibrational frequency wil bev above De. The equi librium bond distance is r 1.2746 A A useful intermolecular potential can be described by the Morse potential which gives the correct shape at small and large interatomic distances. V(r-r.) = De(1-e-3(r-re))2 where r-re is the displacement from equilibrium, β is related to the force constant (bond strength): k = 2.52 De. The energy for the Morse oscillator is (a) Assuming a Morse oscillator, calculate the energy of the n = 0 and n = 1 states. Compare to the harmonic oscillator energies for n 0 and n = 1 states (b) Calculate k and β (c) Plot both the harmonic potential and the Morse potential for HCl (d) On the same plot, show the relative values of the vibrational energies, Eo an E for HCl for both the harmonic and Morse potentials
Consider a diatomic molecule such as HCl. The fundamental vibrational frequency has been measured as v 2991 cm-1. The dissociation energy is De 7.31 x 10-19 J. De is the energy difference between the minimum of the potential well and the separated atoms. Therefore, the lowest vibrational frequency wil bev above De. The equi librium bond distance is r 1.2746 A A useful intermolecular potential can be described by the Morse potential which gives the correct shape at small and large interatomic distances. V(r-r.) = De(1-e-3(r-re))2 where r-re is the displacement from equilibrium, β is related to the force constant (bond strength): k = 2.52 De. The energy for the Morse oscillator is (a) Assuming a Morse oscillator, calculate the energy of the n = 0 and n = 1 states. Compare to the harmonic oscillator energies for n 0 and n = 1 states (b) Calculate k and β (c) Plot both the harmonic potential and the Morse potential for HCl (d) On the same plot, show the relative values of the vibrational energies, Eo an E for HCl for both the harmonic and Morse potentials