We investigate the optical properties of n-type Gallium Nitride (GaN) with concentrations ranging from 5×1016 to 7×1018 cm−3. The near-band edge ultraviolet (UV) transition increases monotonically with the doping concentration. The photoluminescence linewidth of the near-bandgap optical transition increases from 47 to 78 meV as the doping concentration is increased. The broadening is modeled by taking into account potential fluctuations caused by the random distribution of donor impurities. Excellent agreement is found between experimental and theoretical results. We also investigate the origin of the yellow luminescence in GaN. At low excitation densities the experimental ratio of the UV-to-yellow photoluminescence does not change significantly as the doping concentration is increased by two orders of magnitude. Analysis of the luminescence in terms of a theoretical model indicates that the yellow luminescence is due to compensating impurities or defects.