= Solution
The <grafting density> is the inverse area per chain:
$$
\boxed{\Sigma\simeq D^{-2}=0.010\ \mathrm{nm^{-2}}=10^{16}\ \mathrm{m^{-2}}.}
$$
For a neutral <polymer brush> in a good solvent, stretching costs $F_{\rm el}/k_BT\sim h^2/(Nb_0^2)$ per chain while excluded-volume interactions cost $F_{\rm int}/k_BT\sim vN^2/(hD^2)$. Minimization gives $h^3\sim vN^3b_0^2/D^2$. With $v\sim b_0^3$,
$$
\boxed{h\sim Nb_0(b_0/D)^{2/3}=6.84\times10^3\ \mathrm{nm}=6.84\ \mu\mathrm m.}
$$
An isolated good-solvent coil has size $\sim b_0N^{3/5}\simeq502$ nm, much larger than $D=10$ nm, consistent with strong overlap. The brush height is below the 20 μm contour length. This estimate assumes good-solvent excluded volume and locally planar geometry; the source gives neither solvent quality nor particle radius, so a unique curved-brush thickness is not established. An ideal-solvent brush has different scaling.
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