The enzyme nitrogenase contains an ironsulfur cluster, Fe434, where the atoms ofeach type are arranged at the corners of a cube. To model the...

This is a homework question that I could not get the correct answer. I turned it the assignment without completing this question. I need help on part a and b. Thanks.

5. The enzyme nitrogenase contains an iron—sulfur cluster, Fe434, where the atoms ofeach type are arranged at the corners of a cube. To model the bonding in this iron—sulfur cuhe, wavefiJnctions andenergies of the bonding electrons can he described as an elecuompaflicle in a cuhical {three—dimensional} hox whose edges have length a = 3.0!] 131. ’123212122 Energies for 12 3 —D particle in 12 box: 511111an = [71% +71%, + 1232) 11,, = 1,2,3 121, = 1,2,3 n, = 1,2,3 {a} Write the Hamiltonian operator that descrihes an electron in a one—dimensional box and then generalize the Hamiltonian expression for a three—dimensional hox. {h int: Add together theHamiltonian of a one—dimensional hox along each Cartesian dimension to generate a Hamiltonian for a 3—D box} {h} Write a general expression for the quantized wavefiJnctions of an electron in a 3—D box in termsof n1, up, n1, a, x. y, and 2. {hint multiply the waveflJnction of a one—dimensional hox {‘I'IEI] = Esin ($)] along each Cartesian dimension to generate a three—dimensional wave fiJnction ‘F‘ILJ': 2] = ‘F‘IIJ‘FU’J‘FEIJ }- {c} Using the energy expression given above {£3anan construct an energy—level diagram showing the relative ordering of the 11 lowest energy states. Calculate the energy of each level. Lahelthe levels in terms of their quantum nlnnhers and he wary of degenerac ies. {d} Assuming the total numher of valence electrons available is El], place these electrons two at atime in each orbital and show the electron configuration on the plot in part c. {e} If the length of the box is a = 3.11:] 131., calculate the transition energy of an electron fi'om thehighest occupied state to the lowest unoccupied state. What wavelength of light {in nm} willexcite this transition?