[theBuckwheat]

The daughter products of the nuclear reaction of the bomb and the immediate target material have various half-lives. This material is raised aloft and falls to earth in a plume shaped by the wind. Downwind of the bomb, the amount of radiation will be such that people could receive a fatal dose for some days afterwards.

see for example:
All about fallout:
https://archive.org/details/AboutFal1963

http://www.radshelters4u.com/

http://www.ki4u.com/guide.htm

[Farmer Dean]

I was assuming that the fireball never touched the ground.I thought that in that case,the super heated gas from the detonation would be high in the atmosphere.