## 3 Results and Discussion
The spectra were similar, and as an example the experimental spectrum of CeO\({}_{2}\)-Y nanoparticles obtained at room temperature is illustrated in Figure 5a. The spectrum shows a signal at a higher value than the free spin value (g\({}_{\rm{e}}\) = 2.0023), and two signals at lower g values. The EPR signal at g = 2.00935 was assigned to physisorbed oxygen molecules or to paramagnetic species such as \(\bullet\)O\({}_{2}^{-}\) generated from these oxygen molecules [61], and that centred g = 1.964 has been attributed both to quasi-free electrons and to Ce\({}^{3+}\) ions [62]. Both paramagnetic impurities are due to the non-complete stoichiometry obtained during the synthesis process. The effect of the charge separation in semiconducting oxides under irradiation can be probed by EPR. Therefore, the CeO\({}_{2}\)-Y sample was irradiated with UV to check the modification of the spectrum (Figure 5a). Under irradiation, only the resonance signal centred at g = 2.00935 changes its intensity. This behaviour can be explained by the  
Figure 4: The room temperature photoluminescence spectra of undoped and RE-doped CeO\({}_{2}\) (\(\lambda_{\rm{exc}}\) = 325 nm). following: when CeO\({}_{2}\) is irradiated with photons owing energy higher than that of the band gap, electron-hole pairs are generated. If these pairs do not recombine, the electrons are stabilized on cations, while the holes are stabilized by oxygen anions [63]. Thus, the photoexcited electrons are stabilized by Ce\({}^{4+}\) ions, being reduced to Ce\({}^{3+}\); the increases of the resonance signal attributed to this signal are not visible because of the high value of spin orbit coupling and therefore the very fast relaxation time [64]. To illustrate the charge generation and recombination, the intensity of the EPR signal centred at g = 2.00935 was monitored under UV irradiation in three on-off cycles. The obtained kinetic is exhibited in Figure 5b. It can be observed that when the UV is turned on, the EPR signal increased faster and charge carriers stayed at the excited energy level; after turning off the light, the signal decreased, but a little slowly, which means that the recombination process is longer. The on-off cycle experiments show that the process is reversible. The photocatalytic activity of the samples was investigated against Rhodamine B (RhB) solution under visible irradiation. Prior to the photocatalytic experiments, the samples dispersed in solution were kept for 60 min in the dark to achieve an adsorption-desorption equilibrium. The RhB removal rate was monitored by the temporal evolution of RhB absorbance. As an example, Figure 6 shows the evolution in time after dark adsorption and the visible irradiation of RhB absorbance in the presence of the CeO\({}_{2}\)-Gd sample. It could be observed that the RhB absorbance decreases with irradiation time. The decrease in the absorption peak is due to the cleavage of the RhB chromophore ring structure, and the shift of the absorption maximum results in the N-deethylation of RhB molecules [65]. Figure 5: (a) EPR spectra of CeO\({}_{2}\)-Y nanoparticles obtained without and under UV irradiation. (b) Monitorization of \(\bullet\)O\({}_{2}^{-}\) signal under UV irradiation in three on-off cycles. Figure 6: Evolution in time of RhB absorbance after dark adsorption and visible irradiation in the presence of CeO\({}_{2}\)-Gd sample. The RhB removal rate in the presence of all the samples is depicted in Figure 7. All doped samples possess enhanced adsorption capacity relative to ceria nanoparticles. Figure S2 shows the adsorption capacity of Y doped CeO\({}_{2}\) sample for 420 min which proves that after 60 min, the adsorption equilibrium was reached. The enhanced dark adsorption capacity of doped samples could be due to much more active sites for the dye molecules to react. The removal rate of the CeO\({}_{2}\)-Gd sample is almost three times higher than that corresponding to ceria.