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The particle on a ring problem can be used to model electronic transitions in an aromatic hydrocarbon ring (benzene, naphthalene). For a particle on a ring, a particle of mass m is xed to move on a ring of radius a in the xy plane. The Hamiltonian of this system is H^ = ~ 2 2I d 2 d2 , I is the moment of inertia, I = ma 2 and is the angle of the x-axis in the xy plane, which ranges from 0 to 2. a) Find the energy eigenstates for the system. b) Compute the normalization constant for these eigenstates. c) What is the boundary condition for this problem? d) What does this restrict the allowed energies of the system to be? e) What is the degeneracy of the energy levels
Show all the steps in the mechanism for the following reaction, When benzene is mixed with deuterated sulfuric acid, deuterium is slowly incorporated onto the ring. Show the mechanism for this reaction and explain how this relates the sulfonation of ..
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