Born in Shelby, Nebraska, Dunning was educated at the Wesleyan University, Nebraska, and at Columbia University, New York, where he obtained his PhD in 1934. He took up an appointment at Columbia in 1933, being made professor of physics in 1950.

Dunning was one of the key figures in the Manhattan project to build the first atomic bomb. It had been shown by Niels Bohr that the isotope uranium–235 would be more likely to sustain a neutron chain reaction than normal uranium. Only 7 out of every 1000 uranium atoms occurring naturally are uranium–235, which presents difficulties in extraction. Various techniques were tried and Dunning was placed in charge of the process of separation known as gaseous diffusion. This involved turning the uranium into a volatile compound (uranium hexafluoride, UF₆) and passing the vapor through a diffusion filter. As ²³⁵U atoms are slightly less massive than the normal ²³⁸U they pass through the filter a little faster and can thus be concentrated. The difference in mass is so small, however, that simply to produce a gas enriched with ²³⁵U atoms required its passage through thousands of filters. It was largely through gaseous diffusion that sufficient enriched uranium was made available for the bomb to be built.