= Solution
\b[The finite-temperature <Fermi level> lies at the middle of the gap in the stipulated symmetric intrinsic model:]
$$
\boxed{\mu=\frac{E_c+E_v}{2}}.
$$
Here $E_v$ is the valence-band maximum and $E_c$ the conduction-band minimum. Thermal promotion creates one <conduction electron> and one <electron hole>, so <charge neutrality> requires $n=p$. Equal constant densities of states in broad, symmetric bands give equal populations when the distances $E_c-\mu$ and $\mu-E_v$ are equal.
This is a statement about the <chemical potential>, not an available electron state in the gap. Unequal band densities of states would shift the <intrinsic Fermi level> away from exact midgap; the equality follows from the symmetry assumed here.
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