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View submission: ELI5: Why don't atomic explosions "ignite" the atmosphere.
The fear that was briefly held is that it would heat the surrounding air enough for the nitrogen in it to fuse. If this happened, they thought, this might release enough energy for even more nitrogen to fuse. And so on, in a self-sustaining fusion reaction across the surface of the planet.
But it didn't take much calculation to figure out that not only is it hard to make nitrogen fuse (a lot harder than, say, isotopes of hydrogen and lithium, which are what are used in H-bombs), but the reaction would not be self-sustaining at all. Any fusion that did occur would not generate enough heat for the reaction to continue; there are lots of processes by which the heat gets sapped away. In fact making thermonuclear reactions is very very hard even under very controlled conditions.
They did calculations that showed that even if you assume the reactivity of nitrogen is several orders of magnitude higher — that is, if it were thousands of times easier to make nitrogen fuse than it actually is — the heat losses would still be so significant that no reaction of consequence would take place.
How seriously did they take it? I don't think most of them took it very seriously — it was a "flight of fancy" idea that sounded cool at first, but didn't stand up to much scrutiny. However it did stick around as an amusing rumor, sort of a black joke, until the Trinity test.
There's nothing here!