= Solution
The <hydrogenic donor state> radius is the <Bohr radius> rescaled by screening and <effective mass>:
$$
\boxed{a_B^*=a_0\frac{\varepsilon_r}{m^*/m_e}=(0.0529\,\mathrm{nm})\frac{16}{0.2}=4.23\,\mathrm{nm}.}
$$
The <donor-state overlap estimate> compares the mean spacing $n_D^{-1/3}$ to this radius. Taking the spacing as $a_B^*$ gives $n_D\sim(a_B^*)^{-3}=1.32\times10^{25}\,\mathrm{m^{-3}}=1.32\times10^{19}\,\mathrm{cm^{-3}}$. Taking it as the orbital diameter gives a factor eight less, $1.65\times10^{18}\,\mathrm{cm^{-3}}$. Thus a geometric estimate is \b[roughly $10^{18}$–$10^{19}\,\mathrm{cm^{-3}}$], with its contact convention stated. The exponential tails do not have a sharp overlap boundary, and this estimate should not be identified with a precise metal-insulator transition threshold.
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