The ‘unperturbed dimension’ of the polymer chain is represented as,
\[
\left( \overline{r_0^2} \right)^{1/2} \propto \bar{l}\,(n)^{1/2}
\]
where,
\(\left( \overline{r_0^2} \right)^{1/2}\) = root-mean-square end-to-end distance
\(\bar{l}\) = average length of a segment
\(n\) = number of segments in the chain
Using the above information, root-mean-square end-to-end distance of a branched polyethylene would be ........... when compared with that of the linear polyethylene of the same molecular weight and the same number of segments.