in order to check the uniform distribution of nano particles, authenticated characterization is Dynamic light scattering (DLS).The size distribution and average size of the synthesized nanoparticles is determine by using this techniques.
You can use the DLS technique to get size and ( PDI) polydispersity index of the nanoparticle. Then from the PDI you will know if your nanoparticles have uniform distribution or not.
If you want to see how distributed the size of your particles is, DLS should be able to give a quick and easy indication.
DLS measurements are best performed on optically clear samples, so your suspension of nano particles may need to be diluted using the same continuous phase in which it was prepared and placed in a suitable cuvette for whatever DLS instrument that you have access to (assuming that you do).
Most commercial DLS instruments will perform some optimisation to ensure that the instrument optics are suitable set up and a measurement will take upto a couple of minutes.
DLS instruments typically report 2 sets of results for particle size- an average and a distribution.
The Polydispersity index (PI or PdI) that is reported along with the average size can give an indication of the distribution of particle sizes in your sample, with a lower PdI indicating a narrower distribution, with PdI's of below 0.1 typically being reported for a monomeric suspension.
Additionally a size distribution may be reported where peaks indicating the the sizes of all detected particles may be referred to. DLS is comparatively low in resolution compared to counting based techniques so multiple populations may appear as a single broad peak, however this will still give an indication of how uniform a suspension is.