A nuclear explosion is energy being released from a very fast nuclear reaction. It can be caused by nuclear fission, nuclear fusion, or both.
Atmospheric nuclear explosions are associated with mushroom clouds, although mushroom clouds can occur as a result of large chemical explosions. It is also possible to have an air-burst nuclear explosion without these clouds. Nuclear explosions produce radiation and radioactive debris.
The nuclear weapon was first detonated in combat on 6 August 1945, when the United States dropped a uranium gun-type device on the Japanese city of Hiroshima. The second and last use of a nuclear weapon in combat occurred three days later when United States dropped a plutonium implosion-type device on the Japanese city of Nagasaki. These bombings resulted in the immediate deaths of around 120,000 people while more died over time due the nuclear radiation.
Power plant accidents such as those at Chernobyl and Fukushima were caused by steam and hydrogen explosions, not nuclear explosions. The fuel in a nuclear power plant is not enriched enough to create a nuclear explosion.