## 2 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{4}{c}{**Photocatalytic Activity**} & \multicolumn{2}{c}{**MO Degradation**} \\ \cline{2-6}  & \(k_{1}\) & \(R_{1}^{2}\) & \(k_{2}\) & \(R_{2}^{2}\) & **(\%) in 1 h** \\ \hline ZnO & 0.019 & 0.981 & 0.055 & 0.991 & 69.42 \\
3\%Ce/ZnO & 0.038 & 0.988 & 0.226 & 0.991 & 90.43 \\
5\%Ce/ZnO & 0.040 & 0.989 & 0.255 & 0.991 & 92.61 \\
7\%Ce/ZnO & 0.044 & 0.990 & 0.349 & 0.992 & 94.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of the first- and second-order kinetic adsorption rate constants and correlation coefficients of photocatalytic degradation of methyl orange based on the pristine ZnO and Ce/ZnO catalysts. Figure 7: Change in absorption spectra of the **(a)** pristine ZnO, **(b)** 3% Ce/ZnO, **(c)** 5% Ce/ZnO, and **(d)** 7% Ce/ZnO catalysts during photodegradation of methyl orange. First-order kinetic adsorption model:  
\[\ln C_{t}=\ln C_{0}-k_{1}t. \tag{6}\]  
Second-order kinetic adsorption model:  
\[\frac{1}{C_{t}}=\frac{1}{C_{0}}+k_{2}t, \tag{7}\]  
where C\({}_{t}\) and C\({}_{0}\) are the final and initial confirm absorptions of MO under fluorescent lamp illumination, respectively; \(k_{1}\) and \(k_{2}\) are the first- and second-order kinetic reaction rate constants; \(t\) is the fluorescent lamp illumination time. The summary of the calculated \(k_{1}\), \(k_{2}\), \(R_{1}^{2}\), and \(R_{2}^{2}\) was tabulated, as shown in Table 2. It can be seen that the correlation coefficient of the first-order kinetic adsorption model showed a lower value compared with that of the second-order kinetic adsorption model. This indicates that the second-order kinetic model is more suitable and applicable for predicting a kinetic adsorption of photocatalysts in the presence of MO (Table 2). Variations in the reaction rate values indicate that an increase in Ce ion doping in Ce/ZnO catalysts improves the photodegradation reaction. The comparison of photocatalytic MO degradation activity based on Ce/ZnO catalysts is summarized in Table S3. Compared with other reports, our Ce/ZnO catalyst showed a higher photocatalytic activity performance and faster degradation time with 7% cerium. A possible photocatalytic degradation mechanism of the Ce/ZnO catalysts is displayed in Figure 9. The band-edge positions of the conduction (\(E_{CB}\)) and valence band (\(E_{VB}\)) of metal-oxide semiconductors can be calculated using the equations [45]:  
\[E_{CB}=X-E_{c}-0.5\times E_{g} \tag{8}\]  
\[E_{VB}=E_{g}-E_{CB}, \tag{9}\]  
where \(X\) is the electronegativity of ZnO and CeO\({}_{2}\) (5.79 for ZnO and 5.56 eV for CeO\({}_{2}\)), \(E_{c}\) is the free electron energy on the hydrogen electrode scale (4.5 eV), and \(E_{g}\) is the band-gap energy (3.18 for ZnO and 3.00 eV for CeO\({}_{2}\)). According to the conduction and valence band equations, the calculated \(E_{CB}\) and \(E_{VB}\) of ZnO were located at -0.30 and 2.88 eV. In contrast, the calculated \(E_{CB}\) and \(E_{VB}\) of CeO\({}_{2}\) were located at -0.44 and 2.56 eV. A CeO\({}_{2}\)/ZnO heterojunction forms due to the band-edge potentials between ZnO and CeO\({}_{2}\), which is beneficial for photocatalytic activity in terms of preventing charge recombination. Additionally, some Ce\({}^{4+}\) ions may have drifted to the surface of the ZnO, which can promote more trapped electrons by the reaction Ce\({}^{4+}+\) e\({}^{-}\rightarrow\) Ce\({}^{3+}\). The product of this reaction can  
Figure 8: (**a**) First- and (**b**) second-order kinetic adsorption curves of the pristine ZnO and Ce/ZnO catalysts during photodegradation of methyl orange. react with oxygen molecules to form superoxide radicals by the reaction Ce\({}^{3+}\) + O\({}_{2}\)\(\rightarrow\) Ce\({}^{4+}\) + O\({}_{2}^{*-}\)). The generated radicals (superoxide radicals and hydroxyl radicals) then degrade MO and produce oxidized organic products. As a result, it can be seen that an increase in Ce ion doping can improve the photodegradation reaction rate compared with pristine ZnO.