= Solution
The extra <electron> is bound to an approximately singly charged donor through a dielectric-screened Coulomb attraction. In the isotropic <hydrogenic donor state> model, replace the vacuum <electron> mass by $m^*$ and the vacuum permittivity by $\epsilon_r\epsilon_0$:
$$
E_n=-\frac{R^*}{n^2},\qquad
\boxed{R^*=R_H\frac{m^*/m_e}{\epsilon_r^2}.}
$$
At low <temperature>, the donor is mainly in its $1s$ state. Allowed electric-dipole transitions to $np$ states have
$$
h\nu_n=R^*\left(1-\frac1{n^2}\right).
$$
Assign the three printed lines to $n=2,3,4$. Their independently inferred binding energies are
$$
\begin{array}{c|c|c}
h\nu/\mathrm{meV}&n&R^*/\mathrm{meV}\\\hline
7.97&2&7.97/(3/4)=10.6267\\
9.44&3&9.44/(8/9)=10.6200\\
9.97&4&9.97/(15/16)=10.6347
\end{array}
$$
They are mutually close, giving \b[$R^*\simeq10.63\ \mathrm{meV}$]. The <hydrogenic impurity absorption> series accumulates at the donor-ionization limit. \b[Above about $10.6\ \mathrm{meV}$, absorption can place the <electron> in the conduction-band continuum], explaining the continuous spectrum.
Using the supplied $m^*=0.2m_e$ and $R_H=13.61\ \mathrm{eV}$,
$$
\boxed{\epsilon_r\simeq\sqrt{\frac{(0.2)(13.61)}{0.01063}}\simeq16.0.}
$$
The corresponding effective radius is
$$
a^*=a_0\frac{\epsilon_r}{m^*/m_e}\simeq80a_0\simeq\boxed{4.23\ \mathrm{nm}}.
$$
These are the parameters inferred from the printed lines within the stipulated scalar model, rather than substituted tabulated material constants. Real impurity spectra can depart from a single hydrogenic ladder through anisotropy and short-distance impurity effects.<Optical Properties of Solids by Mildred S. Dresselhaus>[Chapter 7, sections 7.2–7.3, printed pp. 76–79: screened hydrogenic levels and departures from the model]{ref}
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