If we predict that l is approximately equal to the bond length observed in benzene (1.39 Å), and substitute the mass of an electron, the speed of light, and Planck’s constant, we can say thatĪpproximately, where is in nanometers. 10 and use the fact that N = p + 3, we have Since the number of bonds between each nitrogen atom is p + 1, if each bond length is estimated to be approximately the same (due to conjugation), say, a length l, then L = (p + 3)l. L for each dye is estimated to be the sum of the length of the carbon chain between the nitrogen atoms and one bond length on each side. Where is the wavelength of maximum absorbance, since a Boltzmann 5 distribution predicts that the wavelength of maximum absorbance will be that of the lowest energy electronic transition (that which occurs between the HOMO and LUMO). Since this transition in these dyes occurs upon absorption of electromagnetic radiation in the visible light region, the most prominent absorbance band for each molecule should be between 380 and 760 nm. In this experiment, the lowest-energy electronic transition of each dye pictured in figure 1 was analyzed using UV-Vis spectroscopy. Since the number of carbon atoms in the chain of each dye is odd, N will always be odd, since N = p + 3 and p is always an odd number. If we let p = the number of carbon atoms in the p system of each dye, it follows that N = p + 3. △ E for the lowest energy electronic transition is that of a transition between the HOMO and LUMO, and is equal toįor the cationic dyes studied in this experiment, there are three p electrons from the two nitrogen atoms, and one p electron for every carbon atom in the chain connecting them. The n-value which corresponds to the HOMO would beĪnd the n-value which corresponds to the LUMO would be According to the Pauli exclusion principal, the number of electrons which occupy any given energy level cannot exceed two, which therefore means that the ground state of any molecule with N p electrons will have filled energy levels if N is even, and filled levels if N is odd. 12) was poor, with ~20% error on average, but when a variable parameter, α, was added, calculations were quite accurate, with 0. 12 and 13 from this model in order to predict, which we compared with experimental data. In this experiment, we have treated each dye as a one-dimensional “particle in a box” in order to simplify the calculation of. Each dye contains a conjugated, hydrocarbon π system with nitrogens at each end, which act as potential barriers for the π electrons in these systems. UV-Vis spectroscopy was used to determine the energy of transition, △ E, from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) of several cationic dyes.
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