## 2 Results and Discussion
The optical absorption coefficient (\(\alpha\)) can be calculated as follows [12; 46; 47]:  
\[(\alpha h\
u)^{2}=D(h\
u-E_{g}), \tag{4}\]  
where \(D\) is a constant which is called the band-tailing parameter, \(h\
u\) is the photon energy, and \(E_{g}\) is the energy band gap. According to Equation (4), the energy band gap of as-prepared materials was calculated by conventional extrapolation of the plot of \(\alpha\) h \(\
u^{2}\) and \(h\
u\) at \(\alpha\) = 0, as shown in Figure 5b. The calculated energy band gaps of the pristine ZnO and Ce/ZnO samples are summarized in Table 1. It can be seen that the optical energy band gap of Ce/ZnO samples decreased with an increase in Ce ion doping from 3.06 (ZnO) to 2.22 eV (7% Ce/ZnO). This indicates that the Ce ion doping helps to tune a narrower optical energy band gap of Ce/ZnO compared to that of pristine ZnO, which tends to be beneficial for photocatalytic activity improvement. Photoluminescence (PL) spectra were studied with the excitation wavelength of 325 nm at room temperature. As shown in Figure 6, the PL spectra of the pristine ZnO and Ce/ZnO samples show an emission peak in the UV region of 387 nm, accompanied by two weaker peaks at 443 and 489 nm. The UV emission can be attributed to the band-to-band radiation of pristine ZnO, which is responsible for photogenerated electron-hole recombination. Two weaker broad emission peaks, which are located in the visible region from 425 to 500 nm, correspond to impurities in the ZnO structure, such as oxygen  
Figure 4: X-ray photoelectron spectroscopy (XPS) spectra of pristine ZnO and 7% Ce/ZnO samples: (a) Survey spectrum and deconvoluted XPS spectrum of (b) Zn 2p, (c) O 1s, and (d) Ce 3d. vacancies and interstitial oxygen [12]. However, luminescent quenching of the Ce/ZnO samples was observed in the order of 7% Ce/ZnO \(>\) 5% Ce/ZnO \(>\) 3% Ce/ZnO \(>\) pristine ZnO. This suggests that an increase in Ce ion doping can reduce charge carrier recombination. Regarding the results, the decreasing charge recombination could be caused by the existence of more defects/oxygen vacancies and the heterojunction between CeO\({}_{2}\) and ZnO. The photocatalytic activities of the pristine ZnO and Ce/ZnO catalysts were evaluated in terms of the degradation of MO under a fluorescent lamp. The fluorescent lamp as a light source contributes to the UV and visible light emissions, as shown in Figure S2. The overlapping area between fluorescent lamp emission and MO absorption was expected to provide photons for photocatalytic reactions. MO degradation was measured by observing the change in the adsorption spectra of MO  
Figure 5: UV–visible spectroscopy of the pristine ZnO and Ce/ZnO samples: (**a**) Absorption spectra and (**b**) optical band-gap energy. Figure 1:0 The photoluminescence spectra of the pristine ZnO and Ce/ZnO samples. at 464 nm, as shown in Figure 1:1 The percentage of MO photodegradation was calculated using the formula [29];  
Figure 1:2  
where \(A_{0}\) and \(A_{t}\) are the initial and final absorbances of MO, respectively. The percentage of MO photodegradation with different Ce ion doping was calculated and tabulated in Figure 1:3 Photocatalysts based on Ce/ZnO showed higher photocatalytic activity, which can degrade 94.06% of MO after 60 min. In contrast, the photocatalysts based on pristine ZnO can degrade 69.42% of MO. The results suggest an improvement of MO photocatalytic degradation due to an increase in Ce ion doping. The mechanism and effectiveness of photodegradation of MO was studied though the kinetic adsorption. Figure 8 exhibits the variation in absorption of the MO solution with the presence of the pristine ZnO and Ce/ZnO samples as a function of illumination time, which was fitted to the first- and second-order kinetic adsorption models, as given by: