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)?

Fill in the blanks with the numbers is a measure of the resistance to flow. a high liquid has a high resistance to flow and flows slowly. the ancients thought everything in the world was made of 4 we now know that there are 94 naturally occurring and scientists have created another 24 i am certain they will create even more. honey flows slowly because it has a high to flowing. a can be separated by physical means because it contains more than one pure substance and 2 pure substances are not chemically bonded to each other. a cannot be separated by physical means. all matter is made up of all elements are with the same number of protons. if it is just a single or many bonded together, if all of them have the same number of protons, it is an element. in a piece of pure iron metal, all the are joined together, that piece of iron metal is called elemental iron. a single of iron is called elemental iron. a mixture has differences from place to place. we might need a microscope to see them or they might be obvious to the unaided eye. there are surfaces separating it into different phases. a mixture is the same everywhere. it is uniform. there are no surfaces separating it into different phases. if different kinds of atoms (different elements) are bonded together by their electrons, it is called a there are physical means of to isolate the different pure substances in a mixture and there are chemical means of to isolate the different elements in a compound. 1. element 2. compound 3. mixture 4. heterogeneous 5. homogeneous 6. pure substance 7. atoms 8. separation 9. viscosity 10. resistance