Nuclear weapons, first created as a result of the Manhattan Project, come in many forms. The ones dropped on Japan, for example, were plutonium and uranium atomic bombs which used nuclear fission (breaking a larger nucleus into two smaller fragments). Hydrogen bombs, on the other hand, use nuclear fusion (fragments combined into a larger nucleus).
Over time, nuclear delivery also improved. Early on, only gravity bombs were used (ex. US bombers circulated around the USSR ready to drop gravity bombs). However, by the time of the Cuban Missile Crisis, rockets and ballistic missiles were developed to carry warheads. Submarine-launchable and backpack nukes also exist.
Because the power of nuclear technology is so great, a policy of Mutually Assured Destruction has been adopted. In other words, both sides don't launch nuclear weapons out of fear that the other side will launch their own.
Currently, there are seven countries known to possess nuclear weapons, and two who are thought to possess them.
For more information, read:Physics 6th Edition by Cutnell and Johnson
The Cold War by Mike Sewell
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