## 2 Materials and Methods  
GO was produced via Hummer's method [18]. In this technique, 3.0 g of graphite powder was combined with 1.5 g of sodium nitrate and 100 mL of concentrated H\({}_{2}\)SO\({}_{4}\) in a beaker in an ice bath. Afterward, 12.0 g of KMnO\({}_{4}\) was gradually added to the mixture and temperature was maintained under 5 \({}^{\circ}\)C. The mixture was stirred for 24 h. After 24 h, 150 mL of deionized (DI) water was poured gradually into the slurry and mixed for another 24 h. Then, 15 mL of 30 wt.% H\({}_{2}\)O\({}_{2}\) was added to the slurry. Finally, the slurry was washed with 5% HCI and DI water multiple times to eliminate the overabundance of metal particles. The obtained brown dispersion was kept in an oven at 90 \({}^{\circ}\)C [15]. At the subsequent stage, GO was reduced with hydrazine hydrate. In this cycle, GO powder was dispersed in DI water (1 mg/mL) and ultrasonicated for 1 h at \(<\)50 \({}^{\circ}\)C to obtain a homogeneous suspension. Next, 2 mL of hydrazine hydrate was placed in 50 mL of the GO solution and pH was adjusted to 10. This solution was stored in an oven at 90 \({}^{\circ}\)C for 24 h. Afterward, the dried rGO powder was washed with DI water and methanol to achieve pH of \(\sim\)7. The rGO suspension was kept in a hot air oven at 60 \({}^{\circ}\)C [22]. The liquid solutions were gamma irradiated under an inert atmosphere at room temperature under the conditions proposed by [PERSON] et al. [17]. A solid mixture of rGO and urea was prepared at a mass ratio of 3:1 (rGO:urea) [23]. Gray powder was added to a mixture of DI water and ethanol. Finally, 10%, 15% and 20% of iron (III) nitrate with a mass ratio of 3:1 (rGO:urea) were taken to prepare the solutions for catalyst synthesis. The range and ratios were adopted from [PERSON] et al. [7], [PERSON] et al. [24] and [PERSON] et al. [25]. Afterward, the solutions were ultrasonicated for 30 min. N\({}_{2}\) was purged into the mixture for 15 min and sealed for irradiation. A \({}^{60}\)Co gamma irradiation source with a total dose of 100 kGy (a dose rate of 2 kGy/h) was used. After irradiation, the mixture was filtered with isopropanol and DI water and dried at room temperature. A catalyst ink was prepared by mixing 10 \(\mu\)L of 5 wt.% Nafion, 100 \(\mu\)L of DIW, 890 \(\mu\)L of ethanol and 2 mg of catalyst. Then, the ink was dispersed in an ultrasonic sonicator for 30 min to acquire a homogeneous suspension. Next, 10 \(\mu\)L of the suspension was drop cast onto a glassy carbon terminal (GCE) and dried at room temperature [21]. Raman spectroscopy (Renishaw inVia Reflex) with an excitation laser of 532 nm wavelength was employed to evaluate the quality of the rGO produced from graphite powder. X-ray diffraction (XRD; Panalytical, X'pert Pro MPD) operated with Cu radiation in the range of 20\({}^{\circ}\) to 70\({}^{\circ}\) was applied to examine the phases of the compositions. A field emission scanning electron microscope (FESEM; Carl Zeiss, GeminiSEM 500) was utilized to explore the surface morphology of rGO and the catalysts. Fourier transform infrared (FTIR) (Bruker Tensor II) was carried out in the range of 700 cm\({}^{-1}\) to 4000 cm\({}^{-1}\). For rotating disk electrode (RDE) measurements, the required electrode was prepared in accordance with previously described methods [26]. Under oxygen (O\({}_{2}\)) saturated conditions, a linear sweep voltammetry (LSV) test was performed with a scan rate of 20 mVs\({}^{-1}\) in a rotation speed range of 400-1600 rpm [23; 24; 25] and in the potential range of 0.1 mV to \(-\)0.8 mV for all three catalysts. Current densities were calculated from LSV and normalized through the geometric surface.