Her professors encouraged her to go to graduate school. She received a fellowship, which enabled her to study radiochemistry with Raymond R. Edwards at the University of Arkansas. At age 19, as an atomic energy research assistant, she received her first Q-level government clearance. In 1952, she married Bill Jewel Good, a fellow graduate student in physics. Mary Lowe Good received her MS in 1953 and her PhD in 1955 from the University of Arkansas becoming the first woman from Arkansas to earn a doctoral degree in the hard sciences. Her graduate work involved studying radioactive iodine in aqueous solutions (used for treating thyroid conditions). She worked on processes of solvent extraction of metal complexes and described the chemical and physical properties of chemical species in an organic solvent. She was able to explain why solutions of radioactive iodine were unstable, and determine the concentration at which species would be at equilibrium values, by applying the Nernst equation effect.