Hall-effect thrusters (HETs) operated with xenon are one of the most commonly used electric propulsion technologies for a wide range of space missions, including drag compensation in low Earth orbit, stationkeeping, and orbital insertion, as access to space becomes more affordable. Although anomalous electron transport, the electron drift instability (EDI), and secondary electron emission (SEE) have been studied experimentally and numerically in xenon-based HETs, the impact of alternative propellants is still poorly characterized. In this work, a two-dimensional particle-in-cell/Monte Carlo collision (PIC/MCC) code is used to model the (r − θ) plane of a HET operated separately with four different noble gases: xenon, krypton, argon, and helium. Models for electron induced secondary electron emission (SEE) and dielectric walls are implemented in order to investigate the coupling between the propellant choice and the radial thruster walls. For all conditions and propellants studied, an EDI and enhanced electron cross-field transport are observed. The frequency of the instability, as well as the electron mobility, are compared with analytical expressions from a recently developed kinetic theory. Confirming this theory, it is shown that while the frequency of the EDI depends on the propellant mass, the electron mobility appears to be almost independent of the propellant choice.