It would be logical to assume that the discovery of fission preceded the invention of the atomic bomb. It would be normal also to expect that no single individual could really claim to be "the inventor", since the possibility sprang naturally from a physical process, and required the efforts of many thousands to bring it into existence. Many descriptions of the origin of atomic bombs can be found that logically and normally say exactly these things.
But they are not correct.
The idea of "invention" does not usually require the physical realization of the invented thing. This fact is clearly recognized by patent law, which does not require a working model in order to award a patent. It is common for inventions to require additional discoveries and developments before the actual thing can be made. In these cases, an invention may fairly have more than one inventor - the originator of the principle idea, and the individual who actually made the first workable model.
In the case of the atomic bomb there is clearly one man who is the originator of the idea. He was also the instigator of the project that led ultimately to the successful construction of the atomic bomb, and was a principal investigator in the early R&D both before and after the founding of the atomic bomb project - making a number of the key discoveries himself. By any normal standard this man is the inventor of the atomic bomb.
This man is Leo Szilard.
On September 12, 1932, within seven months of the discovery of the neutron, and more than six years before the discovery of fission, Leo Szilard conceived of the possibility of a controlled release of atomic power through a multiplying neutron chain reaction, and also realized that if such a reaction could be found, then a bomb could be built using it.
On July 4, 1934 Leo Szilard filed a patent application for the atomic bomb In his application, Szilard described not only the basic concept of using neutron induced chain reactions to create explosions, but also the key concept of the critical mass. The patent was awarded to him - making Leo Szilard the legally recognized inventor of the atomic bomb.
Szilard did not patent this prescient and tremendously important idea for personal gain. His motive was to protect the idea to prevent its harmful use, for he immediately attempted to turn the idea over to the British government for free so that it could be classified and protected under British secrecy laws.
On October 8, 1935 the British War Office rejected Szilard's offer, but a few months later in February 1936 he succeeded in getting the British Admiralty to accept the gift. Szilard's actions in attempting to restrict the availability of the atomic bomb, are also the earliest case of nuclear arms control. Later, when the possibility of a German atomic bomb had been shown to be nonexistent, Szilard campaigned vigorously against the use of the bomb, and went on to help found The Bulletin of Atomic Scientists and The Council for a Livable World.
With the discovery of the neutron by James Chadwick in February 1932 a scientific gold rush ensued to discover what effects would be produced by bombarding different materials with this new particle. Over the next several years, teams of researchers in several countries (especially one headed by Enrico Fermi in Rome) bombarded every known element with neutrons and recorded scores, even hundreds, of new radioactive isotopes.
On May 10, 1934 Fermi's research group published a report on experiments with neutron bombardment of uranium. This was the first such investigation to be reported on. Several radioactive products are detected, but positive identifications were not made. Interpreting the results of neutron bombardment of uranium became known as the "Uranium Problem" since the large number of different radioactivities produced defied rational explanation. The dominant theory was that a number of transuranic elements never before seen were being produced, but the chemical behavior as well as the nuclear behavior of these substances were unexpected and confusing.
The first statement of the correct resolution of the Uranium Problem was published by German chemist Ida Noddack in September. Her letter in _Zeitshrift fur Angewandte Chemie_ argued that the anomalous radioactivities produced by neutron bombardment of uranium may be due to the atom splitting into smaller pieces. No notice of this suggestion was taken.
Fermi discovered the extremely important principle of neutron behavior called "moderation" on October 22, 1934. Moderation is the phenomenon of enhanced capture of low energy neutrons, as when they are slowed down by repeated collisions with light atoms.
December 1935, Chadwick won the Nobel Prize for discovery of the neutron.
In November-December 1938, the Otto Hahn and Lise Meitner correctly unravel the Uranium Problem. Hahn determines conclusively that one of the mysterious radioactivities is a previously known isotope of barium. Working with Meitner, they develop a theoretical interpretation of this demonstrated fact. On December 21, 1938 Hahn submits a paper to _Naturwissenschaften_ showing conclusive evidence of the production of radioactive barium from neutron irradiated uranium, i.e. evidence of fission.
In the first few weeks of January, word of the discovery traveled quickly in Europe.
January 13, 1939 - Otto Frisch observed fission directly by detecting fission fragments in an ionization chamber. With the assistance of William Arnold, he coins the term "fission".
By mid January Szilard heard about the discovery of fission from Eugene Wigner, and immediately realized that the fission fragments, due to their lower atomic weights, would have excess neutrons which must be shed. The multiplying neutron chain reaction that he had postulated had finally been discovered.
January 26, 1939 - Niels Bohr publicly announces the discovery of fission at an annual theoretical physics conference at George Washington University in Washington, DC. This announcement was the principal revelation of fission in the United States.
January 29, 1939 - Robert Oppenheimer hears about the discovery of fission, within a few minutes he realized that excess neutrons must be emitted, and that it might be possible to build a bomb.
February 5, 1939 - Niels Bohr gained a crucial insight into the principles of fission - that U-235 and U-238 must have different fission properties, that U-238 could be fissioned by fast neutrons but not slow ones, and that U-235 accounted for observed slow fission in uranium.
At this point there were too many uncertainties about fission to see clearly whether or how self-sustaining chain reactions could arise. Key uncertainties were:
The different properties of U-235 and U-238 were essential to understand in determining the feasibility of an atomic bomb, or of any atomic power at all. The only uranium available for study was the isotope mixture of natural uranium, in which U-235 comprised only 0.71%.
March, 1939 - Fermi and Herbert Anderson determine that there are about two neutrons produced for every one consumed in fission.
June, 1939 - Fermi and Szilard submit a paper to _Physical Review_ describing sub-critical neutron multiplication in a lattice of uranium oxide in water, but it is clear that natural uranium and water cannot make a self-sustaining reaction. This paper is the first experimental evidence of neutron multiplication.
July 3, 1939 - Szilard writes to Fermi describing the idea of using a uranium lattice in carbon (graphite) to create a chain reaction. This is the first proposal of the graphite moderated reactor concept.
August 31, 1939 - Bohr and John A. Wheeler publish a theoretical analysis of fission. This theory implies U-235 is more fissile than U-238, and that the undiscovered element 94-239 is also very fissile. These implications are not immediately recognized.
September 1, 1939 - Germany invades Poland, beginning World War 2.