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Let's see how well the solution to the one-dimensional particle in a box Schrödinger equation explains the absorption spectrum of a linear conjugated molecule, beta-carotene. The 22 pi electrons (11 double bonds) in this molecule are delocalized over the conjugated system. a) Assume that the energy level solutions to the particle in a line each correspond to an orbital occupied by 2 of the pi electrons with opposite spins. Label the energy levels in the energy level diagram with the energy, expressed in terms of E,=h?/8ma² (for example, E, = 4E,) and %3D populate these energy levels with electrons to form the lowest energy state for the molecule. Hint: Remember to first fully populate the lower energy levels. b) Calculate the energy in Joules of the photon that will excite an electron from your highest occupied energy level to the lowest unoccupied energy level. This will be the lowest energy electronic transition. Use 18.3Å as the effective length of the box.

Let's see how well the solution to the one-dimensional particle in a box Schrödinger equation explains the absorption spectrum of a linear conjugated molecule, beta-carotene. The 22 pi electrons (11 double bonds) in this molecule are delocalized over the conjugated system. a) Assume that the energy level solutions to the particle in a line each correspond to an orbital occupied by 2 of the pi electrons with opposite spins. Label the energy levels in the energy level diagram with the energy, expressed in terms of E,=h?/8ma² (for example, E, = 4E,) and %3D populate these energy levels with electrons to form the lowest energy state for the molecule. Hint: Remember to first fully populate the lower energy levels. b) Calculate the energy in Joules of the photon that will excite an electron from your highest occupied energy level to the lowest unoccupied energy level. This will be the lowest energy electronic transition. Use 18.3Å as the effective length of the box.

Chemistry
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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Let's see how well the solution to the one-dimensional particle in a box Schrödinger equation explains the absorption spectrum of a linear conjugated molecule, beta-carotene. The 22 pi electrons (11 double bonds) in this molecule are delocalized over the conjugated system. a) Assume that the energy level solutions to the particle in a line each correspond to an orbital occupied by 2 of the pi electrons with opposite spins. Label the energy levels in the energy level diagram with the energy, expressed in terms of E,=h?/8ma? (for example, E, = 4E,) and populate these energy levels with electrons to form the lowest energy state for the molecule. Hint: Remember to first fully populate the lower energy levels. b) Calculate the energy in Joules of the photon that will excite an electron from your highest occupied energy level to the lowest unoccupied energy level. This will be the lowest energy electronic transition. Use 18.3Å as the effective length of the box.
Transcribed Image Text:Let's see how well the solution to the one-dimensional particle in a box Schrödinger equation explains the absorption spectrum of a linear conjugated molecule, beta-carotene. The 22 pi electrons (11 double bonds) in this molecule are delocalized over the conjugated system. a) Assume that the energy level solutions to the particle in a line each correspond to an orbital occupied by 2 of the pi electrons with opposite spins. Label the energy levels in the energy level diagram with the energy, expressed in terms of E,=h?/8ma? (for example, E, = 4E,) and populate these energy levels with electrons to form the lowest energy state for the molecule. Hint: Remember to first fully populate the lower energy levels. b) Calculate the energy in Joules of the photon that will excite an electron from your highest occupied energy level to the lowest unoccupied energy level. This will be the lowest energy electronic transition. Use 18.3Å as the effective length of the box.
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