Bohr, the son of Niels Bohr, was born in the Danish capital, Copenhagen, and educated at the university there. After postgraduate work at the University of London from 1942 to 1945 he returned to Copenhagen to the Institute of Theoretical Physics, where he served as professor of physics from 1958 to 1981.

When Bohr began his research career the shell model of the nucleus of Maria Goeppert-Mayer and Hans Jensen had just been proposed in 1949. Almost immediately Leo James Rainwater produced experimental results at odds with the predictions derived from a spherical shell model, and proposed that some nuclei were distorted rather than perfectly spherical.

Bohr, in collaboration with Ben Mottelson, followed Rainwater's work by proposing their collective model of nuclear structure (1952), so called because it was argued that the distorted nuclear shape was produced by the participation of many nucleons. For this work Bohr shared the 1975 Nobel Prize for physics with Rainwater and Mottelson.