$(15\%)$ Estimate a typical radius $(R_g)$ for a random coil of polystyrene $($PS$),$ poly$($ethylene oxide$)($PEO$)$ and polyethylene $($PE$),$ each with $M=100,000\frac{g}{m}ol.$ The statistical segment lengths $(b)$ at $140C$ are $6\mathrm{.}7,6\mathrm{.}0,$ and $5\mathrm{.}9,$ respectively. Why are the dimensions different, given that the $b$ values are so similar?