© 2019 American Physical Society. The DEAP-3600 experiment is searching for weakly interacting massive particles dark matter with a 3.3 ×103 kg single phase liquid argon (LAr) target, located 2.1 km underground at SNOLAB. The experimental signature of dark matter interactions is kilo electron volt-scale Ar40 nuclear recoils producing 128 nm LAr scintillation photons observed by photomultiplier tubes. The largest backgrounds in DEAP-3600 are electronic recoils (ERs) induced by β and γ rays originating from internal and external radioactivity in the detector material. A background model of the ER interactions in DEAP-3600 was developed and is described in this work. The model is based on several components which are expected from radioisotopes in the LAr, from ex situ material assay measurements, and from dedicated independent in situ analyses. This prior information is used in a Bayesian fit of the ER components to a 247.2 d dataset to model the radioactivity in the surrounding detector materials. Pulse-shape discrimination separates ER and NR events. However, detailed knowledge of the ER background and activity of detector components sets valuable constraints on NR backgrounds including neutrons and alphas. In addition, the activity of Ar42 in LAr in DEAP-3600 is determined by measuring the daughter decay of K42. This cosmogenically activated trace isotope is a relevant background at higher energies for other rare event searches using atmospheric argon, e.g., DarkSide-20k, GERDA, or LEGEND. The specific activity of Ar42 in the atmosphere is found to be 40.4±5.9 μBq/kg of argon.