Born at Kitchener in Ontario, Canada, Zinn moved to America in 1930 and received a PhD from Columbia University four years later. He continued research there in collaboration with Leo Szilard, investigating atomic fission. In 1938 he became a naturalized American citizen.

A year later, Zinn and Szilard demonstrated that uranium underwent fission when bombarded with neutrons and that part of the mass was converted into energy according to Einstein's famous formula, E = mc ². This work led him, during World War II, into research into the construction of the atomic bomb. After the war Zinn started the design of an atomic reactor and, in 1951, he built the first breeder reactor. In a breeder reactor, the core is surrounded by a ‘blanket’ of uranium–238 and neutrons from the core convert this into plutonium–239, which can also be used as a fission fuel.