How did the atomic bomb work?

Answer 1

Quite effectively. Or were you referring to mechanism?

"Little Boy" Uranium gun fission bomb (MK-1 design):

1. Fusing mechanism is triggered at preset altitude.
2. Fuse fires electrical primer in breach of gun.
3. Primer ignites bag of smokeless powder.
4. Gasses from smokeless powder accelerate Uranium-235 bullet down barrel.
5. Uranium-235 bullet enters Uranium-235 target on muzzle of gun, forming supercritical mass.
6. Uranium-235 bullet crushes Polonium/Beryllium neutron source, causing a burst of neutrons into supercritical mass.
7. Neutrons cause uncontrolled chain reaction in supercritical mass resulting in explosion.
8. Dense Uranium-238 tamper jacket (now vaporized) around Uranium-235 target holds back explosion for a short period to make it stronger.

"Fat Man" Plutonium implosion fission bomb (MK-3 design):

1. Fusing mechanism is triggered at preset altitude.
2. Fuse initiates "x unit", which generates 32 precisely timed detonator firing pulses, to make all 32 detonators fire at the same time.
3. Each of 32 detonators detonates a shaped charge "explosive lens".
4. Each of 32 explosive lenses focuses spherical expanding detonation wave from its detonator into a spherical contracting detonation wave.
5. The 32 spherical contracting detonation waves from the 32 explosive lenses arrive at the surface of a sphere of high power "booster" explosive, which helps the 32 sections merge into a single spherical contracting detonation wave and adds energy to the wave.
6. When the detonation wave hits the spherical Uranium-238 tamper it becomes a hydrodynamic shock wave, imploding the tamper.
7. When the shock wave hits the Plutonium-239 core it implodes the core assembling a supercritical mass.
8. When the shock wave hits the Polonium/Beryllium neutron source in the center of the core it implodes the neutron source, causing a burst of neutrons into supercritical mass.
9. Neutrons cause uncontrolled chain reaction in supercritical mass resulting in explosion.
10. Dense Uranium-238 tamper (now vaporized) around Plutonium-239 core holds back explosion for a short period to make it stronger.

Answer 2

First we have a minor definition problem with this question: your two usages of "atomic" have different meanings.

• "Atomic bomb" is the popular term for a fission bomb (as "hydrogen bomb" is the popular term for a fusion bomb). But in modern weapons terminology "atomic bomb" and "nuclear bomb" are usually interchangeable and can refer to either fission or fusion bombs. And even the terms "fission bomb" and "fusion bomb" can be ambiguous as almost all modern nuclear bombs use some mix of both fission and fusion. In any case "nuclear bomb" is technically more accurate, as the only part of the atom involved in either fission or fusion is the nucleus.
• "Atomic fission" is a specific nuclear process that occurs in certain isotopes, where the nucleus splits into two nearly equal mass smaller nuclei (statistically most commonly 1/3 and 2/3 mass) either spontaneously or when triggered by neutron capture. This usage of atomic is the generic scientific one used by both chemists and physicists (i.e., the smallest unit of an element).

Anyway I hope that clarifies things and helps you find the answer to the question you really intended to ask.