Calculate the Separation of Energy, Frequency of Radiation, and Probability. Advanced P-Chem Problem.?
To a first approximation, a PI electron in a linear polyene may be considered to be a particle in a 1-D box. Some linear polenes, of which B-Carotene is an example, are important biological co-factors that participate in processes as diverse as the absorption of solar energy in photosynthesis and protection against harmful biological oxidations. B-Carotene contains 22 conjugated Carbon atoms and the average inter-nuclear distance is 140pm. In the ground state, each level up to n=6 is occupied by two electrons.
A. Calculate the separation in energy between the ground state and the first excited state in which one electron occupies the state with n=7.
B. Calculate the frequency of the radiation required to produce a transition between these two states.
C. Calculate the total probability of finding an electron between Carbon atoms 11 and 12 in the ground state of B-Carotene.