## 4 Conclusions  
In summary, CeO\({}_{2}\) nanoparticles doped with rare earth ions (Eu\({}^{3+}\), Gd\({}^{3+}\) and Y\({}^{3+}\)) were synthetized via a green hybrid sol-gel combustion method. The nanoparticles have a face-centred cubic (_fcc_) fluorite structure, and the slight increase in the cell parameters sustains the replacement of Ce\({}^{4+}\) with dopant ions. Undoped CeO\({}_{2}\) has a small crystallite size (around 8 nm) and by doping a slight increase was noticed, except for Y ions. The particle size evaluated by TEM is in accordance with the crystallite size evaluated by XRD, sustaining the formation of monocrystalline particles. By doping the band gap, the energy decreases, which shows that additional levels are introduced by doping into the CeO\({}_{2}\) band gap. The EPR spectra evidence similar behaviour for all doped samples. The intense signal at g\(\sim\)2.0093 was assigned to physisorbed oxygen molecules or to paramagnetic species such as \(\bullet\)O\({}_{2}^{-}\) generated from these oxygen molecules, and a lower one at g\(\sim\)1.964 was due to quasi-free electrons or Ce\({}^{3+}\) ions. Under UV light irradiation, the signal at g\(\sim\)2.0093 increases in intensity, which suggests an efficient charge separation by capturing the photogenerated holes with oxygen anions. The charge generation and recombination processes are reversible. The RhB removal rate was tested under UV light irradiation. The removal of pollutant molecules is due to two processes, adsorption and photocatalysis. The best performance was obtained using Gd-CeO\({}_{2}\), with the adsorption playing an important role. But the best photocatalytic activity was obtained for Y-doped CeO\({}_{2}\). The spin-trapping experiment revealed the generation by Y-CeO\({}_{2}\) nanoparticles of both \(\bullet\)OOH and \(\bullet\)O\({}_{2}^{-}\) radicals involved in RhB photodegradation. In our future works, studies of the photocatalytic degradation of other organic pollutants will be considered.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14020522/s1](https://www.mdpi.com/article/10.3390/app14020522/s1)]([https://www.mdpi.com/article/10.3390/app14020522/s1](https://www.mdpi.com/article/10.3390/app14020522/s1)), Figure S1: HPLC chromatograms of RhB for the initial solution--a; undoped CeO\({}_{2}\)--b; Eu-doped CeO\({}_{2}\)--c; Y-doped CeO\({}_{2}\)--d; Gd-doped CeO\({}_{2}\)--e; Figure S2: The dark adsorption capacity of CeO\({}_{2}\)-Y sample for 420 min.  
Conceptualization, D.T. and A.M.; methodology, D.T., A.P., R.B. and A.M.; investigation, D.T., A.P., R.B., R.B., T.F.M., I.P. and M.F.; writing--original draft preparation, D.T. and A.M.; writing--review and editing, D.T., A.P., R.B.S., T.F.M., I.P., M.F. and A.M.; visualization, D.T., A.P. and A.M.; supervision, M.F. and A.M.; project administration, A.M. All authors have read and agreed to the published version of the manuscript.  
Financial support was provided by a grant from the Ministry of Research, Innovation and Digitalization, CNCS--UEFISCDI, project number PN-III-P4-PCE-2021-1561, and from the MCID through the \"Nucleu\" Programme within the National Plan for Research, Development and Innovation 2022-2027, project PN 23 24 01 03.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflicts of interest.