Radioactive materials (like uranium, which happens to be what I research!) release small particles all the time, this is the process called radioactive decay. These small particles hit other uranium atoms, and cause them to release particles as well. Each time a particle is released, a lot of energy is released as well. So before long there are loads of these particles flying around and smashing into other atoms which gives off huge amounts of energy very quickly.
It is the release of all of this energy that creates an explosion, and it is the radioactive particles that are left behind that are responsible for the poisoning of the people and the land that surround the explosion.
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