## 2 Results and Discussion
The photocatalytic efficiency of the nanocomposites used has been worked out by using Equation (3) [43; 44] as  
\[\%\text{ D}=\frac{[\text{Ao}-\text{At}]}{\text{Ao}}*100 \tag{3}\]  
Figure 6: Percentage of degradation of RhB dye by (**a**) Ce/GOCNIO NPs, (**b**) Yb/GOCNIO NPs; Percentage degradation of MB dye by (**c**) Ce/GOCNIO NPs, (**d**) Yb/GOCNIO NPs. where % D is the degradation in percentage, Ao is the initial absorbance taken at zero time, and At is the absorbance taken at time 't' when the sample was irradiated using a light bulb. Figure 7a,b represent the degradation efficiency of the synthesized photocatalysts. For determining the transfer of charge carriers in semiconductors, the band edge potential can be calculated using well-known equations as  
\[\text{E}_{\text{CB}}=\text{X}-\left(\text{E}_{\text{eff}}+0.5\text{E}_{\text{g}}\right) \tag{4}\]  
\[\text{E}_{\text{VB}}=\text{E}_{\text{CB}}+\text{E}_{\text{g}} \tag{5}\]  
where X, E\({}_{\text{g}}\), E\({}_{\text{CB}}\), and E\({}_{\text{VB}}\) are the expressions of electro negativity, band gap, conduction band edge potential, and valence band edge potential, respectively, whereas Eef is the free e-energy relative to the H-scale (4.25 eV). The band gap for Fe\({}_{2}\)O\({}_{3}\) is 2.3 eV and 2.7 eV for the graphitic carbon nitride material (Table 1), as both materials are key to establishing heterojunctions in nanocomposites for the photocatalytic degradation of dyes. From Figure 8, it is clear that the superoxide radical formation is actually the path for the degradation of dyes because of the high CB potential of Fe\({}_{2}\)O\({}_{3}\), thus converting O\({}_{2}\) to superoxide radicals (O\({}_{2}\)-*). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multicolumn{2}{c}{**Electro-**} & \multirow{2}{*}{**Band Gap**} & \multirow{2}{*}{**Valence Band Potential**} & \multirow{2}{*}{**Conduction Band**} \\  & **Negativity** & & **(eV)** & & **Potential (eV)** \\ \hline Fe\({}_{2}\)O\({}_{3}\) & 5.27 & 2.3 & 2.1 & \(-\)0.13 \\ g-C\({}_{3}\)N\({}_{4}\) & 4.67 & 2.7 & 1.77 & \(-\)0.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Band gap values calculated for g-C\({}_{3}\)N\({}_{4}\) and Fe\({}_{2}\)O\({}_{3}\) semiconducting materials. Figure 7: Efficiency comparison of (**a**) RhB dye and (**b**) MB dye by using Ce- and Yb-based nanocomposites. The major reaction intermediates formed and their degradation activity involved can be expressed as  
\[\text{Fe}_{2}\text{O}_{3}+\text{h}\
u\longrightarrow\text{e}^{-}(\text{Fe}_{2} \text{O}_{3})+\text{h}^{+}\ (\text{Fe}_{2}\text{O}_{3}) \tag{6}\]  
\[\text{e}^{-}(\text{Fe}_{2}\text{O}_{3})+\text{O}_{2}\longrightarrow\text{O}_{2} ^{*-} \tag{7}\]  
\[\text{g}-\text{C}_{3}\text{N}_{4}+\text{h}\
u\longrightarrow\text{e}^{-}(\text {g}-\text{C}_{3}\text{N}_{4})+\text{h}^{+}(\text{g}-\text{C}_{3}\text{N}_{4}) \tag{8}\]  
\[\text{O}_{2}^{*-}+\text{Dye}\longrightarrow\text{Intermediates} \tag{9}\]  
Based on these points, the possible charge transfer mechanism is shown in Scheme 1. A comparison of photocatalytic efficiency was established between literature data as compared to the present results (Table 2). It is evident from the tabulated data that the designed nanocomposites are more effective and efficient as compared to a range of literature reported results for the photo-degradation of MB and RhB dyes. Figure 8: Possible band gaps calculated for (**a**) g-C3N4 and (**b**) Fe\({}_{2}\)O\({}_{3}\) precursors.