The reliability of nanoscale electronic systems is important in various applications. However, they are becoming increasingly vulnerable to atmospheric neutrons. This research conducted spallation neutron irradiations on a Xilinx Zynq-7000 system on a chip using the China Spallation Neutron Source. The results were analyzed in combination with a Monte Carlo simulation to explore the impact of atmospheric neutrons on the single event effects of the target system on chip. Meanwhile, the contribution of thermal neutrons to the chip’s single event effect susceptibility was also assessed. It was found that absorbing thermal neutrons with a 2 mm Cd sheet can protect against the single event effect on the system on the chip by about 44.4%. The effects of B and Hf elements, inside the device, on a single event effect of the Xilinx Zynq-7000 system on chip were evaluated too. Additionally, it was discovered that 10B interacting with thermal neutrons was the primary cause of the thermal neutron-induced single event effect in the system on chip. Although Hf has a high neutron capture cross section, its presence does not significantly affect the sensitivity to single event effects. However, during atmospheric neutron irradiation, the presence of Hf increases the possibility of depositing the total dose in the tested chip.