## 3 Results and Discussion
The photocatalytic process could be described by the first order kinetic model following the equation  
Figure 1:0  
where A\({}_{t}\)--absorbance of RhB at t time; \(A_{0}^{*}\)--absorbance of RhB after dark adsorption; t--irradiation time; and k\({}_{t}\)--apparent kinetic constant. The obtained plots show a linear relationship with the irradiation time (Figure 8). In Table 2 are shown the calculated rate constants and correlation coefficients corresponding to Figure 1:1 From the obtained k values, it can be seen that the best performance was obtained using Y-CeO\({}_{2}\), followed by Eu-CeO\({}_{2}\) > Gd-CeO\({}_{2}\) > CeO\({}_{2}\). The photocatalytic mechanism can be explained based on the formation of electron-hole pairs. Under visible irradiation, electrons absorb energy and move from the valence band to the conduction band, resulting in the appearance of electron-hole pairs. The electrons interact with oxygen and produce superoxide radicals and the holes interact with H\({}_{2}\)O, resulting in hydroxyl radicals. These radicals are known as radical oxygen species and are capable of degrading organic pollutants. The photocatalytic activity depends on  
Figure 1:2 Evaluation of photodegradation kinetic. Figure 1:3 Removal rate of RhB solution in the presence of each sample. the capacity of the photocatalyst to separate the electron-hole pairs. The most important factor is represented by the rate of electron-hole pair separation and recombination. The delay in recombination drives enhanced photocatalytic activity [24]. To evidence the reactive oxygen species, ESR coupled with spin-trapping experiments was performed. The experimental spectrum is shown in Figure 1:4 The obtained spectrum is a complex one, consisting of many resonance lines which are due to several species. To identify the species, a simulation of the spectrum was carried out. The simulated spectrum is also shown in Figure 9 and was obtained through a linear combination of the following spin adducts: \(\bullet\)DMPO-OCH\({}_{3}\) (\(\mathrm{a_{N}}\) = 13.3 G, \(\mathrm{a_{H}^{\beta}}\) = 8.3 G, \(\mathrm{a_{H}^{\gamma}}\) = 1.9 G, relative concentration 60%), \(\bullet\)DMPO-O\({}_{2}^{-}\) (\(\mathrm{a_{N}}\) = 12.9 G, \(\mathrm{a_{H}^{\beta}}\) = 11.4 G, \(\mathrm{a_{H}^{\gamma}}\) = 2.6 G, relative concentration 31%) and nitroxide-like radicals (\(\mathrm{a_{N}}\) = 13.9 G, relative concentration 9%). The proof of the \(\bullet\)OH radical existence in the system is due to the presence of \(\bullet\)DMPO-OCH\({}_{3}\) spin adducts, since these spin adducts are generated by the reaction between \(\bullet\)OH radicals and DMSO solvent [66]. Nitroxide-like radicals were generated by the cleavage of the NAC bond followed by the ring opening of DMPO [67]. The roles of scavengers in elucidating the active radical species involved in photodegradation are to capture and suppress the action of the species under investigation during the photocatalytic process. The scavenger experiment was performed to evaluate the active radical species that participated in the photocatalytic process. Ethylenediamineetraacetic acid (EDTA) and vitamin C (Vit C) were used as h\({}^{+}\) and \(\bullet\)O\({}_{2}^{-}\) radical scavengers, respectively [68]. The scavenger experimental conditions were the same as those used for the RhB degradation and 1.0 mM scavenger was added to the solution. In Figure 10, all samples showed lower RhB degradation than the control experiment (with no scavenger), which attested that these radical species are involved in the photocatalytic process. The dominant active species showed the weakest photocatalytic activity. Therefore, the lowest \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & \(\mathbf{K\times 10^{-3}}\) & \(\mathbf{R^{2}}\) \\ \hline CeO\({}_{2}\) & 0.37 & 0.9860 \\ CeO\({}_{2}\):Eu & 1.13 & 0.9441 \\ CeO\({}_{2}\):Gd & 1.09 & 0.9244 \\ CeO\({}_{2}\):Y & 1.24 & 0.9594 \\ \hline \hline \end{tabular}
\end{table}