The lowest absorption energy of simple organic molecules can often be predicted by approximating the molecule as a 1D particle in a box. Consider the molecule 1,3-butadiene, which consist of four Carbon atoms in a conjugated chain. Butadiene absorbs light at a wavelength of 310 nm. Assume we can model this molecule by only considering its T electrons occupying the energy levels of a 1D particle in a box. Approximating the absorption energy as a highest occupied to lowest unoccupied (HOMO to LUMO) orbital transition, find the size of the "box" that would correspond to an excitation wavelength of 310 nm (you have just found an estimate for the length of the 1,3 butadiene molecule!). Give your final answer in units of angstrom. In your work, also comment on whether you would expect the molecule octatetraene, which contains 8 C atoms in a conjugated chain, to absorb light at a higher or lower wavelength.

The lowest absorption energy of simple organic molecules can often be predicted by approximating the molecule as a 1D particle in a box. Consider the molecule 1,3-butadiene, which consist of four Carbon atoms in a conjugated chain. Butadiene absorbs light at a wavelength of 310 nm. Assume we can model this molecule by only considering its T electrons occupying the energy levels of a 1D particle in a box. Approximating the absorption energy as a highest occupied to lowest unoccupied (HOMO to LUMO) orbital transition, find the size of the "box" that would correspond to an excitation wavelength of 310 nm (you have just found an estimate for the length of the 1,3 butadiene molecule!). Give your final answer in units of angstrom. In your work, also comment on whether you would expect the molecule octatetraene, which contains 8 C atoms in a conjugated chain, to absorb light at a higher or lower wavelength.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

The lowest absorption energy of simple organic molecules can often be predicted by approximating the molecule
as a 1D particle in a box. Consider the molecule 1,3-butadiene, which consist of four Carbon atoms in a conjugated
chain. Butadiene absorbs light at a wavelength of 310 nm. Assume we can model this molecule by only considering
its T electrons occupying the energy levels of a 1D particle in a box. Approximating the absorption energy as a
highest occupied to lowest unoccupied (HOMO to LUMO) orbital transition, find the size of the "box" that would
correspond to an excitation wavelength of 310 nm (you have just found an estimate for the length of the 1,3
butadiene molecule!). Give your final answer in units of angstrom. In your work, also comment on whether you
would expect the molecule octatetraene, which contains 8 C atoms in a conjugated chain, to absorb light at a
higher or lower wavelength.

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