How were the Manhattan Project scientists able to predict the possibility of the atmosphere igniting after using an atomic bomb, and how did they come to the conclusion that the atmosphere wouldn’t ignite?

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Did the non-zero risk of the atmosphere igniting increase as nuclear weapon yields got larger and larger?

Obviously a result of watching Oppenheimer.

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If you pumped enough energy into air (or really, pretty much anything) the atoms that make up the air will fuse together to make heavier elements (Nitrogen combining to make either magnesium and helium or oxygen and carbon). This would release a lot of energy, the same mechanism that makes a hydrogen bomb work. This energy could (potentially) fuel further nitrogen-nitrogen reactions, releasing more energy and so on into an every increasing explosion. This is what they were worried about.

However reaction requires a LOT of energy. As the explosion happens, it expands outward in a sphere, and as it expands the energy spreads out so that the “local” energy in any particular spot drops quickly. Moreover, only a portion (a tiny portion typically) will actually go into making the nitrogen atoms collide and collisions would actually be pretty rare, the actual atoms in air are pretty spread out.

The Mahhatan project scientists calculated the very upper limit for the energies that a bomb would create, along with the very lower bound for when fusion would occur in the atmosphere. From those calculations, they determine that the atomic bomb would not have nearly enough energy to fuse nitrogen. Furthermore, they also calculated that even if nitrogen fusion occurred, the reaction would fizzle out and it would not be enough to fuse more nitrogen. The world was safe.

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