The effect of the characteristic size of nanoparticles, nanofiber (nanowire), and thin films of the AmO2, CmO2, NpO2, PaO2, PuO2, ThO2, and UO2 actinide dioxides on their band gap has been studied quantitatively by a nanothermodynamic method. The size effect is essential in the case of ThO2 nanoparticles, nanofiber, and thin films and NpO2, PuO2, and CmO2 nanoparticles and nanofiber even at a characteristic size of about 20 nm. The size effect is significant for AmO2, PaO2, and UO2 nanoparticles if their diameter is about 7–8 nm. The maximum attainable band gap of nano-objects is shown to be twice the band gap of the corresponding bulk material. The band gap of nano-objects having the same characteristic size decreases in the sequence nanoparticles > (nanofiber) nanowire > thin films. It is shown that, using mixed actinide oxides and varying their stoichiometry, characteristic size, and morphology, one can control the band gap of nano-objects in a wide range of permissible values.