= Solution
<Gallium> has three valence <electrons>, one fewer than silicon, and acts as an <acceptor impurity>. A neutral acceptor can be described as a negatively charged centre binding an <electron hole>. Thermal release of these holes gives a <p-type semiconductor>.
At low <temperature>, the bound hole can absorb far-IR photons in transitions between acceptor levels. The simplest scalar <hydrogenic acceptor state> model predicts
$$
E_n=-\frac{R_A^*}{n^2},\qquad
R_A^*=R_H\frac{m_h^*/m_e}{\epsilon_r^2},
$$
so one expects \b[a discrete bound-hole absorption series followed by a photoionization continuum]. In that idealization, the first lines would be at $3R_A^*/4$, $8R_A^*/9$ and $15R_A^*/16$, with threshold $R_A^*$.
The hole <effective mass> is not supplied, so the <electron> mass $0.2m_e$ cannot be reused to give numerical Ga line positions. In a real <valence band>, multiple hole bands, anisotropic masses and spin-orbit effects can split and complicate the series; acceptor spectra are generally less accurately described by one scalar hydrogenic ladder.<Optical Properties of Solids by Mildred S. Dresselhaus>[Section 7.3, printed p. 79: departures from the hydrogenic model for degenerate valence bands and acceptors]{ref}
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