Question

The 22 de localized TT-electrons in the 11 conjugated C-C bonds which make up the center ß-carotene molecule behave as if they are in a box 2nm long. Given the usual 2 electrons per energy level that you know from chemistry, the highest energy electron (in the HOMO) is in the n = 11 state. What energy photon is needed to bump it to the n = 12 (LUMO) state?

Answer 1

Energy of transition of a particle in 1D box is given by E = [(n- n,? h?] / 8ml? where n = energy state of particle after transition n = energy state of particle before transition h = plancks constant m= mass of electron 1 = length of the box Hence, E = [(122 - 112). (6.62610-34 Js)?]/8 * 9.1 * 101 kg * (2 * 10-ºm)2 E = 3.4677 * 10-19 Thus, we requre a photon of the marked enegry to carry the transition from n= 11 to n= 12.