If you set of a thermonuclear bomb in the middle of the air you'll get a bit of fallout from the primary stage that sets it off, the secondary, fusion, stage wi

If you set of a thermonuclear bomb in the middle of the air you'll get a bit of fallout from the primary stage that sets it off, the secondary, fusion, stage will produce a bunch of neutrons but no fallout, and the third, depleted uranium, stage will absorb all the neutrons from the fusion and produce a fair amount of fallout. A lot of neutrons will escape and interact with the air but none of the elements you find in the atmosphere turns into anything much worse than deuterium or carbon-14 when you whack it with a neutron so overall its fine. You can replace the third stage with lead and lose half the explosive force but gain an almost entirely clean explosion. If you set it off near the ground many of the escaping neutrons will interact with things that get very angry when activated by a stray neutron. A big bomb detonated near the ground, to crack open a bunker for instance, can send stupendous amounts of fallout into the air and kill people hundreds of miles down wind of acute "vomit now and die in a week" radiation poisoning.