This experimental project is a continuation an precision measurement project dedicated to making an atom-interferometric measurement of h/M (where h is Planck's constant and M is the mass of a cesium atom). This measurement will be made at the level of 0.5 ppb, which is more than a factor of ten more precise than previous direct measurements. The measurement can be combined with existing mass measurements to yield a measurement of the fine structure constant at the same level of accuracy. The new value of the fine-structure constant can be compared to a recent independent measurement to make the most precise test of the theory of quantum electrodynamics. The broader impact of this research includes the education of graduate students who will finish their PhDs on this project. Further broader impacts will derive from the fact that methods developed for this experiment strongly advance the state of the art and are thus likely to yield improvements in atom interferometry's many applications, such as navigation, inertial sensing, measurements of local gravity and Newton's constant, and tests of general and special relativity.