= Solution
{c}
A <hydrogenic donor state> has an exponentially decaying envelope $\psi(r)\propto e^{-r/a_b}$. Neighbouring donors at typical separation $r_d\sim n^{-1/3}$ therefore have exponentially small orbital overlap. The corresponding <hopping integral> is of order $E_b e^{-r_d/a_b}$, apart from algebraic factors and factors from the number of neighbours. Hybridizing many such localized states produces an <impurity band> with a <bandwidth> of the same scale:
$$
\boxed{W\sim E_b\exp\left(-\alpha\frac{n^{-1/3}}{a_b}\right).}
$$
The order-one constant $\alpha$ absorbs details of the donor spacing and envelope. The exponential dependence expresses <quantum tunnelling> between weakly overlapping donor orbitals, rather than thermal excitation over the donor binding <energy>.
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