b) For each species, fill the energy levels with the keeping in mind the Pauli -electrons, principle for electron pairing. Identify the quantum number of the highest occupied energy n level of each species. c) Use the highest occupied and lowest unoccupied energy levels to predict the wavelength of light that can be used to excite a from the highest energy occupied state to the -electron lowest energy unoccupied state for each species. d) The molecule in carrots that makes them appear orange is -carotene. Use the particle in a box model to predict the energy gap between the highest occupied state and the lowest unoccupied state. Use this energy to determine the maximum wavelength for absorption of light by Use a length for of = 1850 pm. -carotene. -carotene L trans--carotene Some molecules have cyclic conjugated Benzene and coronene are examples -systems. of such molecules. For molecules with distributions, the quantized energy levels are -electron “circular” given by Eq. 2. (Eq. 2) In this case, the quantum number has integer values between 0 and and is the radius n R of the ring in meters. Unlike the linear particle in a box problem, the circular problem allows for both positive and negative integer values for for clockwise and counterclockwise motion. Also, n for the circular problem, = 0 is an eligible quantum state. For this problem, assume that the ring n radii are 139 pm for benzene and 368 pm for coronene. e) Describe the -electron system using the particle-in-the-ring equation for energy benzene’s levels. Draw a diagram depicting all occupied energy levels as well as the lowest-unoccupied energy level. When building the energy levels, keep in mind the Pauli principle for electron pairing and that there may be several states with the same energy referred to as degenerate states. Make sure that you use the right number of  electrons. Use two significant figures in your answers. f) Now, draw a similar energy level diagram for coronene and calculate the quantized energy values for the occupied energy levels and the lowest unoccupied energy level. Use two significant figures in your answers.
b) For each species, fill the energy levels with the -electrons, keeping in mind the Pauli principle for electron pairing. Identify the quantum number n of the highest occupied energy level of each species. c) Use the highest occupied and lowest unoccupied energy levels to predict the wavelength of light that can be used to excite a -electron from the highest energy occupied state to the lowest energy unoccupied state for each species. d) The molecule in carrots that makes them appear orange is -carotene. Use the particle in a box model to predict the energy gap between the highest occupied state and the lowest unoccupied state. Use this energy to determine the maximum wavelength for absorption of light by -carotene. Use a length for -carotene of L = 1850 pm. trans--carotene Some molecules have cyclic conjugated -systems. Benzene and coronene are examples of such molecules. For molecules with “circular” -electron distributions, the quantized energy levels are given by Eq. 2. (Eq. 2) In this case, the quantum number n has integer values between 0 and and R is the radius of the ring in meters. Unlike the linear particle in a box problem, the circular problem allows for both positive and negative integer values for n for clockwise and counterclockwise motion. Also, for the circular problem, n = 0 is an eligible quantum state. For this problem, assume that the ring radii are 139 pm for benzene and 368 pm for coronene. e) Describe the benzene’s -electron system using the particle-in-the-ring equation for energy levels. Draw a diagram depicting all occupied energy levels as well as the lowest-unoccupied energy level. When building the energy levels, keep in mind the Pauli principle for electron pairing and that there may be several states with the same energy referred to as degenerate states. Make sure that you use the right number of  electrons. Use two significant figures in your answers. f) Now, draw a similar energy level diagram for coronene and calculate the quantized energy values for the occupied energy levels and the lowest unoccupied energy level. Use two significant figures in your answers.
44th_International_Chemistry_Olympiad-_Preparatory_Problems.docx