1 40 Points Our Understanding Of The Behavior Of Electrons Owes Itself To Quantum Mechanics Quantum Mechanics Reve 1 (83.16 KiB) Viewed 62 times
1 40 Points Our Understanding Of The Behavior Of Electrons Owes Itself To Quantum Mechanics Quantum Mechanics Reve 2 (46.66 KiB) Viewed 62 times
(1). (40 points) Our understanding of the behavior of electrons owes itself to quantum mechanics. Quantum mechanics reveals that particles exhibit wave-like properties on the atomic scale, and thus, exist in discrete states with characteristic energy levels. Since the amount of energy an electron can have is non-continuous, it follows that an electron can only gain or lose an amount of energy exactly equal to the difference in energy between its current state and another discrete state. Therefore, molecules and atoms absorb light only when the energy of an impinging light quantum or photon matches the energy difference between the state in which the molecule initially finds itself and some excited state of the molecule. It is, also, known that electrons gain or lose energy in the form of electromagnetic radiation, which of course always has a characteristic wavelength. For Cyanine dye molecules, shown in the figure below, the position (wavelength) and strength (absorption coefficient) of the absorption band depends upon the length of the carbon chain between the nitrogen atoms. diye GUN, H CILCH, 15 dye D A in coefficient (10 cm) 10H cach, н cuck, dye! Dye 200 300 400 500 600 CRCR x anch, HX Dye wavelength inm) Figure.: Absorption spectra of 3 cyanine dyes constructed from data in the paper by W. T. Simpson, J. Chem. Phys. Series A, 1948, 16, 1124. Dye I (A) has 3 carbon atoms and the absorption maximum is at 309 nm, dye II (B) has 5 carbon atoms and the absorption maximum is at 409 nm, and dye III (C) has 7 carbon atoms and the absorption maximum is at 512 nm.
(a). Assume that the molecules are linear and use the values 135 and 154 pm for the C=C and C-C bonds; 147 pm and 128 pm for the C-N and C=N, respectively, to calculate the box length of these dyes. (b). Sketch and label an energy level diagram showing the occupied energy levels and the first unoccupied one of these conjugated electron movement in the dyes. (c). Write an expression for the energy of first absorption transition of the dyes (d). Using the free electron molecular orbital model, what is the wavelength (in nm) of light required to induce a transition from the ground state to the first excited state of each of the three dyes? Compare your wavelength calculations here to the experimental values on the figure above (i.e., what are the percentage errors). NB: If possible, use table to summarize your answers
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