  The discrepancy between the theoretically calculated and experimentally
measured activation gaps in quantum Hall effect has long been a puzzle. We
revisit this issue in the context of the $\nu=1$ quantum Hall state, while also
incorporating the skyrmion physics. We find that the finite width and the
Landau level mixing (LLM) effects are not sufficient to explain the observed
activation gap. We further show that the presence of charged impurities located
adjacent to the quantum well can cause a significant reduction in the
activation gap, while also causing a suppression of the skyrmion size.
