The p, orbitals of carbon atoms in a benzene ring are pi electrons that can be...

 

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The p, orbitals of carbon atoms in a benzene ring are pi electrons that can be considered to be free (and non-interacting) and confined in a circle of radius R corresponding to the C-C resonance bond (1.39A). There are 6 such pi electrons from the 6 carbon atoms in the molecule. a) Find the longest wavelength that benzene molecule will absorb (due to transition of an electron from the highest occupied level to the next level) as per this simple model. Of course, note that due to Pauli exclusion principle any state can accommodate only 2 electrons. Compare your answer with the experimentally observed absorption peak at an approximate wavelength of 268 nm. b) Though in the class I used for this particle on a ring example, position x along the circumference as the variable, a more natural variable would be the angular position The wavefunction of the free particle then can be written down as (p)-ee Find the allowed values of n and hence allowed values of energies. = The p, orbitals of carbon atoms in a benzene ring are pi electrons that can be considered to be free (and non-interacting) and confined in a circle of radius R corresponding to the C-C resonance bond (1.39A). There are 6 such pi electrons from the 6 carbon atoms in the molecule. a) Find the longest wavelength that benzene molecule will absorb (due to transition of an electron from the highest occupied level to the next level) as per this simple model. Of course, note that due to Pauli exclusion principle any state can accommodate only 2 electrons. Compare your answer with the experimentally observed absorption peak at an approximate wavelength of 268 nm. b) Though in the class I used for this particle on a ring example, position x along the circumference as the variable, a more natural variable would be the angular position The wavefunction of the free particle then can be written down as (p)-ee Find the allowed values of n and hence allowed values of energies. =