We have used tunnelling spectroscopy (TS) to probe the density of states (DOS) of the rare earth manganate Nd0.5Sr0.5MnO3, which shows a transition to a charge ordered (CO) antiferromagnetic insulating state from a ferromagnetic metallic state. We find that a gap opens up in the DOS around the Fermi level, E-F, as the solid is cooled below the charge ordering temperature T-CO. The charge ordering gap (Delta(CO)) was found to be strongly temperature dependent for T approximate to T-CO and for T/T-CO < 0.6 it reaches a limiting value of nearly 0.27 eV. Above T-CO the temperature dependence of the DOS at E-F was found to be similar to that of the solids such as La0.8Ca0.2MnO3 which show colossal magnetoresistance but no charge ordering.