How far does a nuclear bomb travel?
This is dependent on many variables including yield, weather, height of burst, "salting" of the tamper, etc.Your question can't be answered without knowing these.
The idea that these bombs explode because of the range of effects is nonsense.Nuclear bombs do not explode during the assembly of a supercritical mass.
There are effects that can reach thousands of miles under the right conditions.
The initial blast of a nuclear bomb causes it to go outward.It can leave the drop zone.There would be fires and radiation at that point.The water quickly evaporated.