For a linear polymer molecule, the total chain length $L$ depends on the bond length between chain atoms $d=0\mathrm{.}154nm,$ the total number of bonds in the molecule $N,$ and the angle between adjacent backbone chain atoms $109,$ as follows: $L=$Ndsin$(\frac{}{2})$

Furthermore, the average end$-$to$-$end distance for a series of polymer molecules $r$ is equal to: $r=d\sqrt[\phantom{2}]{?}N$

For a linear polytetrafluoroethylene determine $($PTFE$)$ with Atomic weights for Carbon $=12\mathrm{.}01g\frac{r}{m}ol$ and F$,$ Fluorine, $A=19g\frac{r}{m}ol$ :

$($a$)$ the number$-$average molecular weight for a linear polytetrafluoroethylene of total length L$=1000$ nm

$($b$)$ the number$-$average molecular weight heavily twisted and kinked polymer with average endto$-$end distance $r=15\mathrm{.}5nm/$