The DEAP-3600 experiment is searching for WIMP dark matter with a 3.3 tonne single phase liquid argon (LAr) target, located 2.1 km underground at SNOLAB. The experimental signature of dark matter interactions is keV-scale $^{40}$Ar nuclear recoils (NR) producing 128 nm LAr scintillation photons observed by PMTs. The largest backgrounds in DEAP-3600 are electronic recoils (ER) induced by $beta$ and $gamma$-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. While excellent discrimination between ERs and NRs is reached with pulse shape discrimination, utilizing the large difference between fast and slow components of LAr scintillation light, detailed knowledge of the ER background and activity of detector components, sets valuable constraints on other key types of backgrounds in the detector: neutrons and alphas. In addition, the activity of $^{42}$Ar in LAr in DEAP-3600 is determined by measuring the daughter decay of $^{42}$K. 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 $^{42}$Ar in the atmosphere is found to be $40.4 pm 5.9$ $mu$Bq/kg of argon.
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