The idea that matter contained lots of possibly practicable releasable energy came with an understanding of what radioactivity was and how E=mc^2 applied to making sense of it. That understanding more or less started to gel with people like the Curies and Rutherford and Soddy. Soddy's The Interpretation of Radium (1909) set off a lot of discussion about the energy releasable if one could make radioactive transformations happen en masse and at will, and inspired H.G. Wells to coin the term "atomic bombs" in The World Set Free (1914).

However there was no mechanism for releasing that energy on command, much less all at once. The discovery of the neutron (1932) led Leo Szilard to hypothesize the neutron-based chain reaction (e.g., a reaction that could be started by one neutron but produce two or more as a consequence) in 1933 (and was in part inspired by Szilard's reading of Wells) but no such reaction was known to exist so he didn't really get anyone excited by the idea.

In late 1938, a team of German-Austrian scientists (Hahn, Strassman, Meitner, Frisch; the latter two separated geographically from the former two because of political strife in the world) discovered nuclear fission, the splitting of uranium atoms by neutrons. They announced this publicly in early 1939. Their work was surprising though the research they were doing (shoot neutrons at stuff and see what happens) had been undertaken since the mid-1930s (they were in fact replicated and reinterpreting an experiment done by Fermi and his team in 1935).

Szilard immediately realized that this might be a candidate for the neutron-based chain reaction, since it was started by neutrons. He immediately began searching for "secondary neutrons" (neutrons produced by fission reactions) and found they existed. Other scientists (Joliot-Curie in France, for example) also began similar observations. Dunning in the US determined that it was only the U-235 atom that was fissioning, and Bohr and Wheeler articulated a theory of fission that explained why it was happening (and why some isotopes did it and others did not). So by mid-1939, the possibilities of nuclear technology, either as reactors or maybe bombs, were known globally. However the feasibility was not at all clear, because only the rare U-235 isotope was known to fission, and it was not clear that they could practicably separate it from the more common (99%) U-238 isotope with which it is always found.

By the end of 1939, physicists in several countries (the USA, France, the UK, Germany, and the USSR) had petitioned their governments for funds to study this problem. There were immense uncertainties still about every angle of the problem, and it was largely not treated as an urgent issue. The real "breakthrough" was a report from the UK written in 1940 where two physicists (Frisch and Peierls) determined that the total amount of U-235 needed to make a weapon was relatively small (on the order of a 10 lbs) and that the explosion from such a purified approach would be massive (on the order of tens of thousands of tons of TNT). Further study in the UK produced the recommendation that while the UK could not build such a weapon in time for use in the now-ongoing war with Germany, but that the Germans might be able to do it, and that the Americans might be able to do it.

Through a series of complicated events, top scientist-administrators in the US became aware of and convinced of the importance of this report in the summer of 1941. They also became aware of the discovery of an artificial element, plutonium, which also seemed fissionable, and could be produced using a nuclear reactor. They mobilized their own plodding research program into first a pilot program (the prove that the basics were possible), and then, in late 1942, a production program dedicated to manufacturing nuclear weapons in time for use in the war. This latter program, which was run by the US Army Corps of Engineers, is what we call the Manhattan Project.

There is a bit of irony here. The US was spurred by a UK report that was exceedingly optimistic, it turned out, about the ease at which this work could be done. In fact it proved quite difficult, taking more time and more resources to produce workable atomic bombs. They pulled it off, but just barely — a few months later and they might not have had weapons in time to use before the end of the Pacific war (and they missed the European war entirely). The Germans, as it turned out, decided at the same time (1942) that it was too difficult and too risky to attempt such a program, and so focused entirely on getting a pilot reactor program working (and they failed at this). The German estimate of the difficulty was, in fact, pretty spot-on correct — but they didn't think they'd need a bomb (they felt they were winning the war) and they didn't fear anyone else making one.

Anyway, that's the basic timeline. There are other layers of complexity in terms of decision-making, what was known and not known at various times, and so on. It is not a small story, and the scientific work spanned continents, and the actual industrial work of producing the bomb (the Manhattan Project) ended up requiring the labor of hundreds of thousands of people, at literally hundreds of sites across the USA (and some sites in the UK, Canada, and even further overseas), and billions of dollars of funding, and so on.

For further reading: If you would like a very close coverage of the early scientific discoveries, Rhodes' The Making of the Atomic Bomb still holds up. If you would like a nice description that integrates the science and the more policy questions a bit better, B. Cameron Reed's The History and Science of the Manhattan Project is excellent on this front, as well.

Hi there -- you may be interested in this section of our FAQ, in particular the AMA with u/restricteddata about the history of the Manhattan project.