To echo other comments: The nucleus of an atom is made up of protons and neutrons, which attract each other with what is often called ‘strong nuclear force.’ This attraction holds so much energy it actually *reduces* (think of it as borrowing) part of the mass of the nucleus to hold itself together (aka ‘mass defect’).
When that nucleus is forced to break up (in nuclear reactions like fission or fusion) then some of that binding force (the mass being borrowed as energy for the strong nuclear attraction) gets converted to pure energy. This conversion, famously depicted as “e = m* c^2” means that part of the mass defect in the nucleus gets multiplied by the speed of light times itself, and the resulting energy is released as photons at the site of the reaction.
In real-world, non-nuclear scale, that means a tiny amount of matter gets converted into an enormous amount of radiation in a matter of milliseconds. Some of that radiation makes it out as radio, infrared (heat waves), light, gamma rays, and everything in between, but a lot of that radiation gets absorbed by the fuel for the reaction, the casing or housing, and the air/water surrounding it. That material can only take so much energy before it turns to gas or plasma and explosively expands in any direction it can. This part happens at the speed of light, and is visible as a flash.
That causes another, thermal chain reaction of gas and plasma hitting matter *slightly* farther away, and causing it to turn into hot gas and plasma as well. The total energy being released is so great that it will keep doing this until it stops agitating matter to higher, luminous states that emit more energy- the limit of matter getting agitated and expelling more heat and light is what is visible as a slowly-growing ‘fireball’. It is the hottest, and ironically *least* destructive part of a nuclear explosion.
The next effect is what happens in terms of matter getting moved around by the blast, essentially at the speed of sound rather than light. All that air getting turned to plasma and hot, luminous gas means it’s expanding and pushing other air out of the way. A LOT of mass of air has to make way for a very small mass of it, which suddenly needs to take up a HUGE volume. This overpressure is what causes the shockwave seen in videos, a massive wind blast at hurricane forces and above, extending for kilometers, much MUCH further than the relatively small fireball. The majority of damage from the two bombs used in war, and the rest of the tests, is from this massive displacement of air or water, caused by the rapid expansion of the small amount of matter in the immediate vicinity of the fireball.
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