air burst will eradiate the ground over which it burst and all the debris from the destruction you retard. All that will be sucked into the air and distributed down wind.
But it won't be sucked into the fireball, and, therefore, radiation won't contaminate it.
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The character of the radiation received at a given location also varies with the distance from the explosion.
[21] Near the point of the explosion, the neutron intensity is greater than the gamma intensity, but with increasing distance the neutron-gamma ratio decreases. Ultimately, the neutron component of the initial radiation becomes negligible in comparison with the gamma component. The range for significant levels of initial radiation does not increase markedly with weapon yield and, as a result, the initial radiation becomes less of a hazard with increasing yield. With larger weapons, above 50 kt (200 TJ), blast and thermal effects are so much greater in importance that prompt radiation effects can be ignored.
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It was found in early experimentation that normally most of the neutrons released in the cascading chain reaction of the fission bomb are absorbed by the bomb case.
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So, if we are not talking about ground bursts or some exotic things like "neutron bombs" or "cobalt bombs" or "strategic gigaton-class torpedoes", and ignore non-calculatable (and, in short-run, unimportant), climate effects, the only important thing is the blast-caused devastation. It's a terrible thing, of course, but nothing really apocalyptic.