For calculating the average sizes of QDs by UV spectra, you may first calculate the band-gaps of QDs via UV-visible absorbance spectra, or diffuse-reflection spectra. And you should also know the bulk band-gaps and dielectric constants of CdSe, CdS, etc. Then, you can use the Brus Equation to carry out the particle-size calculation.
For detailed information about Brus Equation, please see the attached picture. : )
First you calculate the band gap of the material by plotting hν Vs (αhν)n. If you know the effective mass of the electrons and holes of the material, the particle size can be calculated from the Brus Equation