Ok so the top comment is saying things both correct and incorrect.
Fusion based bombs do not create dangerous daughter nuclei (on purpose) because they burn deuterium and tritium (via lithium) to produce very energetic helium nuclei.
However, in the case-ulam-teller design (Ivy Mike, and other early H-bombs) there is a uranium or plutonium tamper that encases the fusion fuel. This high-Z material reflects neutrons and radiation back into the fusion fuel.
Basically, to create a fusion reaction with a self sustained burn you need excellent confinement of energy. The easiest way to do this is to make the fuel dense enough that neutrons and photons are reabsorbed instead of escaping the system.
So in the CUT H-bomb a traditional fission bomb is set off to increase radiation pressure and heat the fusion fuel, which then begins to fuse until the kinetic pressure is so great that the encasing radiation reflector explodes.
In short, there is a very large amount of fall out from an H-bombs, but considerably less than a fission bomb of the same explosive magnitude.
*I don’t have any knowledge of thermonuclear bomb design past the 60s because that is all classified
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