Shannon received his B.S. and M.S. degrees in Ceramic Engineering from the University of Illinois in 1957 and 1959. He then went on to receive his Ph.D. in Ceramic Engineering from the University of California at Berkeley in 1960. He then joined the DuPont Company as a research chemist from 1964 to 1971 where he concentrated on high-pressure synthesis and precious metal oxide chemistry. He then spent 1971 conducting post-doctorate studies at McMaster University in Hamilton, Ontario, working with Chris Calvo on the crystal structures of a number of vanadates and with David Brown on bond strength-bond length relationships useful in determining H locations in hydroxides and hydrates.  Next, he took a sabbatical leave from DuPont and spent 1972 at the CNRS and teaching at the University of Grenoble, France as a visiting professor, where he presented a course on solid state chemistry and conducted research on high-pressure chemistry of vanadates. He returned to DuPont in 1973 to do research on new ionic conductors and precious metal oxide chemistry.
In 1982, he was granted another sabbatical leave from DuPont and worked on catalysis with zeolites at the Institute de Catalyse in Lyon, France. Upon completion of the sabbatical, he returned to DuPont and worked for another ten years before retiring in 1992.
After retirement, he received a grant from the Alexander von Humboldt Foundation to continue his research on ion polarizabilities in collaboration with Reinhard Fischer in 1994 at the Universities of Mainz and Bremen in Germany and with Olaf Medenbach at the Ruhr-Universität in Bochum, Germany. There, he prepared three papers on refractive indices and electronic polarizabilities in oxides, and other compounds. He has since moved to Colorado where he has been associated with the University of Colorado Boulder · Cooperative Institute for Research in Environmental Sciences (CIRES).
Shannon was a member of the American Chemical Society and the American Crystallographic Association. He was elected a Fellow of the Mineralogical Society of America. He has served on the Evaluation Panel for Materials Science at the National Bureau of Standards, and on the National Science Foundation Subcommittee for Oversight Review of Solid State Chemistry.