No; because the bomb was detonated so high in the atmosphere, nuclear radiation only spread fifty-three hundredths of a kilometer at Hiroshima, and one and one thousandth of a kilometer at Nagasaki (1). Even though radiation can travel globally, how far it spreads depends on many factors. Radiation from Japan if a meltdown occurs in one of the reactors could affect the United States. However, it would still not have a very significant impact on our cancer levels because radiation weakens over distance. Thus, people near nuclear disasters are at a far greater risk than those distanced from it.
The citation in the other answer is from a school essay made available to students to cheat. I question its reliability. Significant radiation was measured 2 km from the hypocenter at Hiroshima (first link). Deaths from cancer attributed to radiation occurred in people 2.5 km away (second link).
The point that such radiation does not travel very far and remain strong, is valid.
That specific piece of information from the essay was attributed to another work.
Radioactive particles do not become less radioactive simply because they travel a great distance. They may become more spread out, or as in the case of iodine, which has a short half life, lose radiactivity, but particles such as strontium do not become less radioactive for thousands of years. That is a point that we need to clear up. There is a greater risk of more exposure the closer you are, but there is still a risk from a radioactive particle, no matter how far it traveled to reach your skin or your lungs or the soil you garden in.
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