Dempster was born in Toronto, Ontario, in Canada and educated at the university there. He emigrated to America in 1914, attended the University of Chicago, obtained his PhD in 1916, and began teaching in 1919. In 1927, he was made professor of physics.

He is noted for his early developments of and work with the mass spectrograph (invented by Francis W. Aston). In 1935, he was able to show that uranium did not consist solely of the isotope uranium–238, for seven out of every thousand uranium atoms were in fact uranium–235. It was this isotope, ²³⁵U, that was later predicted by Niels Bohr to be capable of sustaining a chain reaction that could release large amounts of atomic fission energy.