## 3 Results and Discussion
### Photocatalytic Activity  
HfO\({}_{2}\)-graphene nanocomposites are novel, and there are no earlier reports on their photocatalytic activity to date. The universal method of assessing a nanocomposite photocatalyst activity is by measuring the time dependence of the concentration loss of an organic compound such as MB dye under UV irradiation. To investigate the photocatalytic activities of the bare HfO\({}_{2}\) and HfO\({}_{2}\)-graphene nanocomposites with varying amounts of graphene (10, 30, and 50 wt%) with different reaction times (0, 30, 60, 90, 120, 150, and 180 min), a photodegradation study was performed by using MB dye under UV light irradiation (Figure 7). The prepared nanocomposite, before and after irradiation, was used to measure the degradation efficiency of MB dye (D%) by the following equation [58]. \[\text{D}\%\ =\ \times 100 \tag{4}\]  
where C\({}_{0}\) = MB initial concentration and C = the catalyst concentration at particular time interval after irradiation. Figure 7a gives the UV-Vis absorption spectra for HfO\({}_{2}\)-graphene (50 wt%) 40 mg catalysts composite. Whereas out of various combinations of composites, Figure 7a shows that HfO\({}_{2}\)-graphene (50 wt%), whereas 40 mg catalyst composites show a significant decrease in the absorbance and, hence, a sizeable photodegradation efficiency. Figure 7b depicted that the decomposition of MB dyes using HfO\({}_{2}\)- graphene catalyst at various weight ratios, such as 10, 20, 30, 40, and 50 mg, and the corresponding decomposition efficiencies were 35%, 57%, 73%, 99%, and 94% at 180 min. The best performance of the loading catalyst is 40 mg for the maximum decomposition of HfO\({}_{2}\)-graphene. The catalyst's ability to remove large amounts of MB dyes is 40 mh, and it is impaired by the  
Figure 6: (**a**) UV-Visible absorption spectra of HfO\({}_{2}\) nanoparticles, graphene, and HfO\({}_{2}\)-graphene (10, 30, and 50 wt%) nanocomposites, (**b**) Variation of (ahv)\({}^{2}\) with photon energy for graphene and HfO\({}_{2}\) and HfO\({}_{2}\)-graphene (10, 30, and 50 wt%) nanocomposites. light reflection of the catalyst particles [56]. Degradation at different concentrations of MB dyes has been analyzed. The variation of C/C\({}_{0}\) vs. time of exposure is depicted in Figure 7c, and it is observed that the photocatalytic efficiency increases with the increasing content of graphene. It is worth noting that the HfO\({}_{2}\)-graphene composites (50 wt%) of 40 mg show a significantly improved photodegradation efficiency related to MB dye compared to the rest of the composites, achieving complete degradation in 180 min under UV light irradiation with a sharp fall-off at 180 min marking 99% of degradation. This abrupt enhancement of photocatalytic activity in the HfO\({}_{2}\)-graphene composites (50 wt%) may be due to the excellent distribution of HfO\({}_{2}\) particles in the graphene matrix. This may be due to the creation of intermediate energy levels, thus minimizing the bandgap. The recycled runs investigated the catalyst stability performance of the HfO\({}_{2}\)- graphene nanocomposite in removing the MB dyes with the recovered catalyst, as shown in Figure 7d. It is essential to conduct the recyclability test of the prepared photocatalyst for practical applications. Under UV light irradiation, the synthesized HfO\({}_{2}\)-graphene nanocomposite assessment was made for the photodegradation of MB dye. The decrease in the effectiveness of degradation for the dye for three recycling tests was shown, thereby showing the repeatability of the photocatalytic activity and the notable stability of the HfO\({}_{2}\)-graphene nanocomposite as a catalyst. The degradation performance for five cycles shows a small decrease, and the  
Figure 7: UV-vis absorption spectra of MB solution during the photodegradation under UV light.