= Solution
The <correlation length> in a semidilute solution is the <concentration blob> size. Below it a chain retains isolated good-solvent statistics; beyond it concentration fluctuations are screened and many chains interpenetrate. It is a local scale, not the total chain <radius>. If a blob contains $g$ segments,
$$
\xi\sim ag^{3/5},\qquad \phi\sim\frac{ga^3}{\xi^3}.
$$
Eliminating $g$ gives the <good-solvent concentration-blob scaling>
$$
\boxed{g\sim\phi^{-5/4},\qquad\xi\sim a\phi^{-3/4}.}
$$
Using the supplied segment size and concentration,
$$
\boxed{\xi\simeq0.5\,\mathrm{nm}\,(0.01)^{-3/4}\simeq15.8\,\mathrm{nm}.}
$$
Here $g\simeq316$ and $N/g\simeq32$, so there are many segments within each blob and several dozen blobs per chain. Also $\phi/\phi^*\simeq16$, consistent with a semidilute estimate rather than isolated coils. The cancellation of $N$ from $\xi$ is physical: once chains are long enough, the local concentration sets the mesh scale. As throughout the scaling argument, numerical amplitudes are not determined by the given data.
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