= Solution
\b[The model predicts $I\simeq8.28\ \mathrm{eV}$.] For a uniform ten-site cyclic <Hückel method> model,
$$
\epsilon_j=\alpha+2\beta\cos\!\left(\frac{2\pi j}{10}\right).
$$
Ten <pi electrons> fill $j=0,\pm1,\pm2$ with two electrons per orbital. The <Homo> is the degenerate $j=\pm2$ pair, so
$$
I\simeq-\epsilon_H=-\alpha-2\beta\cos(72^\circ)
=6.8+4.8(0.309017)=\boxed{8.283\ \mathrm{eV}}.
$$
This is the prediction for the stipulated planar conjugated ring. It does not assert that an unconstrained all-cis ten-membered ring actually adopts a strain-free planar geometry.
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