In 1949, Glendenin earned his Ph.D. from the Massachusetts Institute of Technology. That same year he joined Argonne National Laboratory, where he worked until his retirement in 1985.
He published extensively on the properties of fission products. He served as Scientific Secretary for the U.S. delegation to the Atoms for Peace Conference and received the American Chemical Society's Glenn T. Seaborg Award for Nuclear Chemistry in 1974.