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a) The vibrational wavenumber of a diatomic molecule in its electronic state is 2600 cm¬1, whereas that in the first excited state is 2000 cm-1. The separation in energy between the minima in their respective potential energy curves of these two electronic states is 5.0 eV. Calculate the 3 lowest energy transitions originating from the n=0 vibrational state of the electronic ground state to the vibrational states of the excited electronic state. (The potential energy curves of both electronic ground and excited states can be represented by harmonic oscillators.)

a) The vibrational wavenumber of a diatomic molecule in its electronic state is 2600 cm¬1, whereas that in the first excited state is 2000 cm-1. The separation in energy between the minima in their respective potential energy curves of these two electronic states is 5.0 eV. Calculate the 3 lowest energy transitions originating from the n=0 vibrational state of the electronic ground state to the vibrational states of the excited electronic state. (The potential energy curves of both electronic ground and excited states can be represented by harmonic oscillators.)

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a) The vibrational wavenumber of a diatomic molecule in its electronic state is 2600 cm-1, whereas that in the first excited state is 2000 cm-1. The separation in energy between the minima in their respective potential energy curves of these two electronic states is 5.0 eV. Calculate the 3 lowest energy transitions originating from the n=0 vibrational state of the electronic ground state to the vibrational states of the excited electronic state. (The potential energy curves of both electronic ground and excited states can be represented by harmonic oscillators.) b) Consider the quenching of an organic fluorescent species with To = 6.0 ns and ką = 3.0x10$ dm³ mol-1 s-1. Predict the concentration of quencher required to decrease the fluorescence intensity of the organic species to 50% of the unquenched value.
Transcribed Image Text:a) The vibrational wavenumber of a diatomic molecule in its electronic state is 2600 cm-1, whereas that in the first excited state is 2000 cm-1. The separation in energy between the minima in their respective potential energy curves of these two electronic states is 5.0 eV. Calculate the 3 lowest energy transitions originating from the n=0 vibrational state of the electronic ground state to the vibrational states of the excited electronic state. (The potential energy curves of both electronic ground and excited states can be represented by harmonic oscillators.) b) Consider the quenching of an organic fluorescent species with To = 6.0 ns and ką = 3.0x10$ dm³ mol-1 s-1. Predict the concentration of quencher required to decrease the fluorescence intensity of the organic species to 50% of the unquenched value.
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