The Q weak experiment has tested the Standard Model through making a precise measurement of the weak charge of the proton (Q p W ). This was done through measuring the parity-violating asymmetry for polarized electrons scattering off of unpolarized protons. The parity-violating asymmetry measured is directly proportional to the four-momentum transfer (Q 2 ) from the electron to the proton. The extraction of Q p W from the measured asymmetry requires a precise Q 2 determination. The Q weak experiment had a Q 2 = 24.8 ± 0.1 m(GeV 2 ) which achieved the goal of an uncertainty of ≤ 0.5%. From the measured asymmetry and Q 2 , Q p W was determined to be 0.0719 ± 0.0045, which is in good agreement with the Standard Model prediction. This puts a 7.5 TeV lower limit on possible "new physics". This dissertation describes the analysis of Q 2 for the Q weak experiment. Future parity-violating electron scattering experiments similar to the Q weak experiment will measure asymmetries to high precision in order to test the Standard Model. These measurements will require the beam polarization to be measured to sub-0.5% precision. Presently the electron beam polarization is measured through Møller scattering off of a ferromagnetic foil or through using Compton scattering, both of which can have issues reaching this precision. A novel Atomic Hydrogen Møller Polarimeter has been proposed as a non-invasive way to measure the polarization of an electron beam via Møller scattering off of polarized monatomic hydrogen gas. This dissertation describes the development and initial analysis of a Monte Carlo simulation of an Atomic Hydrogen Møller Polarimeter. Clearly good ol' Charlie Brown didn't know about graduate school because my dissertation is way more than a thousand words; but like him, there have been many people who have supported me. I would like to thank my adviser, David Armstrong, for all the help and guidance during my time at William & Mary. I am extremely grateful for all the time he has given to answering my questions and helping me through everything here. Thanks also to the members of my committee Dave Gaskell, Joshua Erlich, and Todd Avertt for help on various components of my work. I would also want to acknowledge my undergraduate teacher, adviser, and mentor, Michael Olson, without whom I would have never realized physics was interesting and pursued experimental nuclear physics. His advice and guidance at St. Norbert College and after has been invaluable and instrumental. I was given many opportunities for teaching, mentoring, and doing research and indispensable lab skills that I otherwise wouldn't have gotten. Also thanks for all the time dedicated to helping, working on research, and developing new labs for classes. I can't thank him enough for his amazing capacity for fostering confidence, giving perspective when needed, and the advice and support he has shared with me over the years and the ones to come. To the people whom I owe my existence, my parents David and Jola Gray. Thanks for all the unwavering support ov...