= Solution
Using $E_\gamma=hc/\lambda$ and an ideal band-edge <photon> energy equal to the quoted gap,
$$
\boxed{\lambda_{\alpha}=\frac{1239.84\ \mathrm{eV\,nm}}{3.4\ \mathrm{eV}}
=364.66\ \mathrm{nm}}.
$$
At low <temperature> an <electron> and <hole> can form a bound <exciton>. Its recombination releases approximately $E_g-E_B$, so its wavelength is longer than $hc/E_g$ evaluated using the gap at that same <temperature>. <GaN> excitation and emission measurements resolve such excitonic transitions below the fundamental gap.<Fundamental energy gap of GaN from photoluminescence excitation spectra by Bo Monemar>[Photoluminescence-excitation, reflection and emission comparison; separation of <exciton> transition energy from the fundamental gap]{ref}
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