ABSTRACT A Low Energy Linear Accelerator (LELIA) is being developed at Hampton University. LELIA is part of a new collaboration between the Physics Department and the Accelerator Division of the Department of Energy funded Thomas Jefferson National Accelerator Facility (Jefferson Lab). The latter graciously provided a 100 keV electron gun that was transferred to the University in January 2012. We have performed a preliminary investigation of the radiation budget for LELIA using the electromagnetic packages of the Geant4 Monte Carlo simulation toolkit. A realistic description of the gun and current laboratory space was modeled in order to estimate future appropriate shielding for this accelerator. The results from this work are described in this dissertation.