The crystallization methods/parameters are very important as far as the quality of ZnO nanoparticle is concern. If so, You will be getting a peak at ~ 370 nm.
If not, there will be an additional broad absorption peak in the visible range.
The spectrum of ZnO nanoparticles depends on method of fabrication, size , shape and temperature. Several methods of fabrication result in ZnO nanoparticles that present exciton peak in the range of 360-380 nm
Range of UV- Vis spectrum of ZnO nanoparticles is 350-380nm. But there is no optimum exciton peak of ZnO nanoparticles. Further validation of optical properties ZnO nanoparticles can be conducted by measuring the bandgap value by utilizing Tauc plot and also measure the urbach energy level.
350nm-390nm is general range to observed absorption spectra but it varies with several factor such as ,Doping Concentration,Method of Prepration ,Contaminants