The short explanation is that because the bombs at Hiroshima and Nagasaki were AirBursts (that is, they were detonated high above the ground), they did not produce significant long-term contamination on the ground.
The long explanation requires a little more exposition:
There are two types of radioactive threats from nuclear weapon.
The first is known as “prompt” radiation. This is a bright burst of radiation that fires out immediately when the bomb detonates. It consists of neutrons and gamma rays. If you get too many of these, you get very sick and die of radiation poisoning within a few weeks.
If you get a pretty high dose but don’t die, you have an increased long-term cancer risk.
If you get a low dose, you get a slightly elevated long-term cancer risk.
For bombs on the order of those at Hiroshima and Nagasaki, you basically have to be within 2 km of where the bomb detonated to be seriously affected by this radiation.
It is worth noting that if you are within such a radius you have a much higher chance of getting killed in some other way (such as from the heat or the blast effects). About 20% of the total deaths of Hiroshima and Nagasaki are attributed to prompt radiation effects.
The second are residual radiation effects. These are caused by two things. The first is the aforementioned blast of neutrons. Neutrons have the special property of being able to make other elements radioactive (induced or artificial radioactivity).
So some of the things those neutrons hit become a bit radioactive. The level of radioactivity from such a thing is not especially high except maybe near the very epicenter of the bomb blast, and even then it is the sort of thing that would be cleared out in not too long. So people walking immediate through the epicenter area might have been exposed to radiation that way.
The other way is what is known as “Fallout”. Atomic bombs work by splitting up of atoms of Uranium or Plutonium (Nuclear Fission). Those split halves, known as fission products, are the remaining parts of the reaction, are very radioactive. The range from being “so radioactive they will kill you almost instantly” to “radioactive enough to give you cancer over several decades.” Keep in mind that the more radioactively energetic a substance is, the less time it sticks around. So the “so radioactive they kill you quickly” stuff is around for a week or so at most. The “will give you cancer” stuff can be around for decades and decades. Some of the elements are truly long-lived by human scales (e.g. Plutonium has a half-life of 24,000 years) but remember that this means that it is not extremely radioactive. You don’t want chronic exposures to low-levels of radioactivity — e.g. in your food or water supply, or embedded in your bones — but short-term exposures will not affect you much.
So the atomic fireball, as it detonates, contains these very radioactive fission products, as well as unreacted nuclear fuel (uranium or plutonium, both long-term radioactive contaminants). This radioactive fireball, however, rises very high into the air — forming the head of the familiar mushroom cloud.
Which gets us to the important point: there are two very different possibilities here. If the fireball does not touch the ground, this hot, radioactive ball of death goes up very high — into the stratosphere — within minutes. It then cools considerably, and looks like a cloud, but is still pretty hot, both thermally and radioactively.
The winds blow it over a vast area, but its heat, and the lightness of the particles, keep it in the area for several weeks. After several weeks, it “falls out” down to Earth, but by that point it has been dispersed over thousands and thousands of square miles, and many of the hottest radioactive by-products have already decayed. From a health standpoint it is near negligible — at most a statistical cancer increase in a large population, probably indistinguishable from background sources.
But if the fireball touches the ground, it is a very different situation. If the fireball touches the ground, it will suck up a huge amount of dirt and debris into that radioactive flame. This has the effect of making the dirt and debris radioactive, both from induced radioactivity and because the fission products will attach themselves to the dirt particles.
These particles are relatively large — you could view them with a microscope, sometimes even with the naked eye — and they are heavy (compared to regular fission products and debris, which are vaporized atoms and thus very tiny indeed). So they “fall out” within hours. This produces the kinds of fallout plumes we have come to associate with nuclear testing: swathes of the ground which are made quite radioactive indeed, producing short-term hazards for people who live there as well as long-term contamination problems.
All of which gets us to the answer to your question: the fireballs at Hiroshima and Nagasaki did not touch the ground. The weapons were detonated high above the ground — not, mind you, because it reduced the radioactivity, but because the ideal blast height to destroy civilian structures is as an airburst. The side-effect, though, is that there was essentially no fallout of significance, and as a result, no serious radioactive contamination of the city.
The above explanation is given by Reddit user : retricteddata. It is put here just to help users who don’t use reddit and missing the awesome parts of web. If you were satisfied with the answer go thank him.