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> Science is cheap.

Indeed. Sustained nuclear chain reaction was achieved in Chicago Pile-1 beneath the stands of campus football stadium at the end of 1942. That's when, scientifically, it was proven that the bomb is possible.

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Pedantic point, that's when they proved nuclear power was possible. It was still unknown whether the cross section of U-235 was large enough to permit a small, transportable bomb to go critical, and whether that reaction would have occurred fast enough to generate a significant explosion. And in the case of Plutonium, the idea of implosion hadn't even been worked out yet, let alone tested.

By 1942 no one really had doubts about that. I mean, the Einstein–Szilard letter was written in 1939 and Bohr mentioned in lectures also in 1939 the bomb is possible but he didn't think it was possible to produce enough weapons grade uranium within the timeframe of the war. He couldn't foresee, no one could, really, what the US could do when determined.

These details were covered in depth in The Making of the Atomic Bomb by Richard Rhodes. The Oppenheimer movie glosses over a lot of the technical details. It’s worth a read.

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