Make a sketch of the radius of gyration of a polymer chain vs. the degree of polymerization N as it would appear on a log-log scale for: (a) a bad solvent, (b) a good solvent, and (c) a theta solvent. If the apparent log-log trend is linear, what is the significance of the slope?

If the temperature were raised very high, classically what would we expect the heat capacity per object to be for this one-dimensional system? give a numerical value. chigh t = __ j/k/object (one reason for the discrepancy is that the high-temperature limit assumes that the number of oscillators is large (n > > 1), which is not the case in this tiny system.)

Suppose you increase your walking speed from 7 m/s to 13 m/s in a period of 2 s. what is your acceleration?

How do you know how many valence electrons an atom has?