He was the joint winner of the 1961 Nobel Prize in Physics (together with Rudolf Mössbauer) "for his pioneering studies of electron scattering in atomic nuclei and for his consequent discoveries concerning the structure of nucleons".

He also received a Charles A. Coffin Foundation Fellowship from the General Electric Company, which enabled him to attend graduate school at Princeton University, where he earned his M.S.

[7] His doctoral dissertation was titled "Infra-red absorption by light and heavy formic and acetic acids.

Robert Hofstadter coined the term fermi, symbol fm,[15] in honor of the Italian physicist Enrico Fermi (1901–1954), one of the founders of nuclear physics, in Hofstadter's 1956 paper published in the Reviews of Modern Physics journal, "Electron Scattering and Nuclear Structure".

Stanford University's Department of Physics credits Hofstadter with being "one of the principal scientists who developed the Compton Observatory.