Bonus10points - Bonus 10 points problem 113A Fall 2011 Your...

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Bonus 10 points problem, 113A, Fall 2011 Your Name: The color green: Chlorophyll is a green pigment found in green plants. It is a Mg complex whose structure is shown below. We can apply the model of particle in a two-dimensional box to model the electrons in the chlorophyll. a) There are 32 resonating -electrons in chlorophyll. Please find the quantum numbers n x and n y corresponding to the HOMO and the LUMO in chlorophyll. Hits: remember that we have a square box, and keep the state degeneracy in mind. For your convenience, we started filling up the table with quantum states in the order of increasing energy. Keep filling this table until you find the desired molecular orbitals and the corresponding n x and n y . You might need to do calculations in order to figure out the correct order of states. State # n x n y Degeneracy 1 1 1 1 2 1 2 2 1 2 3 2 2 1 4 3 1 1 3 2 5 3 2 2 3 2 Etc… b) Using the approximate dimensions of chlorophyll shown above, calculate the energy for
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