What is the expectation value of p2 (the momentum squared)? You can give your answer as an integral (you don"t need to evaluate it). Absorption spectrum of benzene Benzene has 6 pi electrons which can be considered to be delocalized over the molecule. As a crude model of the electronic motion, we can consider these 6 electrons to be moving freely in a two-dimensional square box, 3 angstroms on a side.
A) What is the ground state (lowest energy state) of the molecule? What energy does the ground state (counting all 6 electrons) have?
B) What is the first excited state (next highest energy state) of the molecule? Draw a diagram indicating which orbitals the electrons are in, and label the states with their quantum numbers.
C) What is the energy gap between these two states? Justify why we expect benzene to be primarily found in the ground state when the temperature is room temperature.
D) Calculate the wavelength of light absorbed by benzene in making the transition from its