Presently we explore absorption and emission spectra of ZnO semiconductor nanolayers 4.1-17.3 nm thick. We report that their absorption spectra have discrete structure, with the transition band density increasing with the nanolayer thickness. The emission spectra recorded at 4.1 and 9.3 nm thickness have resolved band structure, with the bands partially overlapping in the 9.3 nm sample. On the other hand, the emission spectra are strongly overlapped in the 13.1 and 17.3 nm samples. We used our modeling approach that considers electronic states in a one-dimensional infinite potential well, calculating the relative electron mass of 0.205, and the starting quantum number for the absorption transitions of 7, 8, 9 and 9, for the respective samples. We also discuss the present results using the traditional approach of solid-state physics, considering potential surfaces in the linear momentum space.