1. The polyyne molecules CkH2 with alternating triple and single carbon-carbon bonds represent potential nanowires for molecular electronics. They can be modelled as linear 1D-boxes with 2k ?-electrons occupying degenerate energy levels in fours (4 electrons per level). For decapentayne (k=10) do the following: (a) Calculate the box width from a proper combination of its C?C and C-C bond lengths (1.21 and 1.38 Å, respectively). From the number of ?-electrons obtain the quantum number n for the highest energy level occupied by electrons. Assuming that electron is on a C atom when being between the middles of the two carbon-carbon bonds to this atom, calculate and compare the probabilities for the electron to be (1) on the innermost C atom and (2) on the C atom next to the outermost one. (b) How do these probabilities change when the electron undergoes transition to the next higher-energy level (show by calculation)? (c) Calculate wavelength ? corresponding to the above transition in (b).