This video was created by the IRSN (the official French Institute for Radiological Protection and Safety); it shows the spread of radioactive cesium137 from the destroyed and burning Chernoybyl nuclear power plant, which burned for more than 14 days in the spring of 1986. Note that the radiation also made its way to China and the US (this map is limited in that it does not show where the radiation travels beyond its borders).
In other words, the plume from a burning or destroyed nuclear reactor does not travel in a straight line, and can contaminate entire continents. A famous English lord pointed out that Europe would be uninhabitable now if nuclear reactors had been built there before World War II. Likewise, if North Korea destroys South Korean or Japanese nuclear power plants with its conventional missiles, the ensuing radioactive fallout from the destroyed reactors and fuel ponds would make much/most of those nations uninhabitable).
Map of radiation exclusion zones and control zones caused by the Chernobyl disaster
CIA Factbook, Sting (vectorisation), MTruch (English translation), Makeemlighter (English translation) – http://www.lib.utexas.edu/maps/belarus.html, specifically http://www.lib.utexas.edu/maps/commonwealth/chornobyl_radiation96.jpg and File:Tchernobyl_radiation_1996.svg for the vector version, see Wikpedia https://simple.wikipedia.org/wiki/Chernobyl_disaster#/media/File:Chernobyl_radiation_map_1996.svg
According to the key in the map, the 1100 square mile uninhabitable exclusion zone that surrounds the destroyed Chernobyl reactor is defined by how much ceisum-137 there is per square kilometer. The exclusion zone has greater than 40 Curies of radioactivity per square kilometer. For those more familiar with square miles, that would be 104 Curies per square mile
One gram of cesium-137 has 88 Curies of radioactivity.
Thus, as little as 1.2 grams of cesium-137, made into microparticles and distributed as smoke or a gas over and area of one square mile, will make that square mile uninhabitable for a century or longer.
Less than two grams of cesium-137, a piece smaller than an American dime, if made into microparticles and evenly distributed as a radioactive gas over an area of one square mile, will turn that square mile into an uninhabitable radioactive exclusion zone. For example, Central Park in NYC (1.3 square miles) can be made uninhabitable by 2 grams of microparticles of cesium-137.
There are immense quantities of cesium-137 stored in the spent fuel pools of the 104 US commercial US nuclear power plants. These pools all currently store, on average, 5 to 7 times more radiation than is found inside the reactor core.
These pools are located outside the primary containment vessels that surround the nuclear reactors. The pools were not originally designed for long-term storage of nuclear waste, but because the US has not created a viable underground repository for nuclear waste, the spent fuel remains on site at the power plants in stainless steel lined pools that are about the size of a tennis court. These pools must be constantly cooled 24/7 by large cooling systems, or else the heat from the intensely radioactive used uranium fuel rods will heat the water to boiling.
If the water were to boil off, or be released from the pool, the rods would be exposed to air and steam. This would cause the rods to overheat, rupture, and in some cases ignite. By the time the rods heat to the point of rupture, much of the cesium-137 in the rods is converted to a gas, thus it escapes. This is what caused the lands around Chernobyl to become uninhabitable.
Nuclear power plants produce much more cesium-137 than do nuclear detonations. The following graph will give you an idea of how much more. Some spent fuel pools contain more cesium-137 than was released by all atmospheric nuclear weapons tests combined. This is why they are considered to be major potential targets for terrorist actions.
They certainly are at risk during war time, for example, there are 15 nuclear reactors in Ukraine, where a civil war is now going on.
Most US commercial nuclear power plants have 1000 to 2000 pounds of Cs137 stored on-site in their spent fuel pools. For example, there are more than 2000 pounds of Cesium137 (that equates to 91 million Curies of Cs137, or close to 1 million grams) in the spent fuel rods in the spent fuel pool at Callaway Nuclear Power Plant in Missouri, which is not far from where I live.