Consider a polymer formed by connecting n disc-shaped molecules into a one-dimensional chain. each molecule can align along either its long axis (of length 2a) or short axis (length a). the energy of the monomer aligned along its shorter axis is higher by ε. that is, the total energy h=εu, where u is the number of monomers standing up. a) calculate the partition function, z (t, n), of the polymer. b) find the relative probability for the monomer to be aligned along its short or long axis. 3. calculate the average length, (l(t, of the polymer. 4. obtain the variance, (l(t, n)(t, n))^2. 5. what does the central limit theorem say about the probability distribution for the length l(t, n)?