Question: Using $N$ for the number of monomers in a chain, $M_0$ for the molecular weight of a single monomer, and $M$ for the molecular weight of the chain,

$($a$)$ what is the relation between $N,M,$ and $M_0?$

$($b$)$ See the table below.

What is the relationship between the drag coefficient $K_D($referred to in the table as friction coefficient$)$ and the diffusion constant, i$.$e$.$ diffusivity, $D?$

$($c$)$ What is the physical interpretation of ${}_1,$ the longest relaxation time of a chain?

$($d$)$ How does the root mean square end to end extension $R$ scale in terms of $M$ for an ideal chain, a chain in good solvent, and a chain in theta solvent?

$($e$)$ In the table $HI$ stands from hydrodynamic interaction. Derive the nine relations for the first three rows. You can ignore the last row on intrinsic viscosity. A Gaussian chain is another term for the ideal chain.