Calculate the root mean square end$-$to$-$end distance of poly$($vinyl chloride$)$ given that the

length of a C$-$C single bond is $1\mathrm{.}54,$ the carbon$-$carbon bond angle is $109\mathrm{.}5,$ and the

molecular weight of the polymer is $1$million$\frac{g}{m}ol($assume the polymer is monodisperse$),$

using the following models:

A$.$ Freely$-$jointed chain

B$.$ Freely$-$rotating chain

C$.$ Hindered$-$rotating chain

The following quantity has been tabulated for poly$($vinyl chloride$)$:

$[\frac{1+(\text{:}cos\text{:})}{1-(\text{:}cos\text{:})}]=1\mathrm{.}8$