$(10$ points$)$ Consider a melt of Gaussian chains with degree of polymerization $N$ and $=1.$

The polymer self$-$concentration $SC$ in the melt is the ratio of the occupied $(V_{\text{o}\text{c}\text{c}})$ volume to

the pervaded volume $(V_p).$ Assuming that nearly all of the monomers are contained within a

spherical volume with radius $R_g,$ derive a scaling relation for $SC$ in terms of $N.$

Does your answer surprise you?