They can be relatively clean(never perfectly clean), or extremely dirty. Depends on detonation altitude and what the secondary tamper is made out of. The fusion releases a lot of neutrons, and this can be used to split depleted uranium, which increases yields but is also very dirty.
With an airburst the contamination is only the material the bomb is made of, and it’s so finely divided that it takes weeks to fall out of the atmosphere, by which point the worst isotopes have already decayed and the rest have been diluted. With a ground level detonation, a lot of relatively heavy material gets contaminated and falls out of the air nearby, posing an immediate hazard.
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