3. Consider the dimethylpolyene dodeca-2,4,6,8,10-pentaene which contains 12 carbons and ten delocatized r-electrons (five pi-bonds). Assume the chain has a length of 15.1A. a. Draw an energy diagram for this system, indicating the HOMO and LUMO and including electrons with spin. b. Calculate the energy and wavelength for the HOMO to LUMO transition. c. Would the wavelength of light needed to induce a transition in the dimethylpolyene tetradeca-2,4,6,8,10,12-hexaene (a 14-carbon linear polyene with twelve delocalized electrons) be longer or shorter than that of dodecapentaene? Provide support for your