Time, Distance, and Shielding
These are the three cardinal factors to controlling exposure. Used "religiously" in the nuclear industry, and applicable to any and all hazardous materials.
One needs to understand that there is a tremendous difference between material being in an area, and humans being exposed. And differences in the kinds of exposure. The two basic types of exposure are internal and external. ALL exposure from nuclear waste, fallout, etc. is external, until you get it into your body. Some of the nuclear byproducts are particularly hazardous, because our bodies take them up easily. The radioactive iodines are very dangerous, short term, because our bodies actually accept them in preference to regular iodine. ANd once in the body, the entire energy emmission affects tissue. But, as mentioned, the half life of radioisotopes of iodine is measured in days (some in hours), so in 6 months they are effectively gone. Some isotopes are never taken in by the body. Krypton gas is one. Others, like plutonium, if ingested or inhaled will remain in the body for ever. Chelating agents (like Zinc-DPTA) have shown promise, and will remove heavy metals from your system, along with all the other metals, which you need for survival.
We have had more than half a century of people being conditioned to be scared of anything with the word "nuclear" or "atomic" attached to it. From THEM to GODZILLA to THE CHINA SYNDROME movies have used atomic energy to create monsters and disaster. Comic book heroes and villians were created by radiation of one kind or another. We have been trained to fear radiation.
Chernobyl was a disaster, certainly true. But it was deliberate. It was NOT an accident in the regular sense. It was not a "leak". Because of the Soviet system, the engineer in charge was not a nuclear engineer, but an electrical engineer, who deliberately had safety systems disabled and bypassed so that a "test" could be conducted, to determine how long the reactor would continue to generate power, and how much, after a total loss of coollant. Warned by plant operators that this was not a good idea, under the Soviet system of management, his was the authority, his word was boss. Things didn't go exactly as he expected. Perhaps, had he been more familiar with the operation of the reactor, it might have been different. Perhaps, if they had not been in the Soviet Union, he might have been overruled. Doesn't really matter now, except as a footnote in history. It is worth remembering however, that the "accident" at Chernobyl was not simply a design flaw, or a failure of critical valves or safety systems, but a deliberate test, outside the design parameters of the systems, that went horribly wrong. The only thing it has in common with the accident at Three Mile Island is that they both happened at nuclear reactors.
That was a very nice map posted earlier, showing the contamination zones at Chernobyl, but it doesn't really say much on a practical level. The measurements of radioactive (Cesium, etc.) materials are in Curies. Curies is a measurement of the amount of material based on it's activity. One Curie of Cesium is a different mass than one Curie of Plutonium, or one Curie of tritium. A useful number for some applications, but not quite as useful for determining how hazardous to human occupation an area is. For that, dose rate units are more useful. Readings in R /hr or better yet REM/hr give much better and more easily understood information about how hazardous a given area is.
One thing you have to give the Soviets, when they go, they go big. In the long run, it caused more harm to the US nuclear industry (including the defense nuclear industry) through public fear and political action as a result of that fear, than just about anything else the Soviets could have done.