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As I have realised, most of the Uranium and Plutonium inside an Atomic Bomb do not actually fission together, even if the critical mass is used. In fact, for Little Boy, only 1.09 kg out of 64 kg of the uranium fissioned, while Fat Man only had 1 kg out of 6.19 kg of plutonium fissioned. Eventually, nuclear fusion is used to compensate for this low conversion, atomic bombs stuffed in nuclear bombs to make more destruction.

I do not fully know what causes this to happen. I initially believed it to be something to do with the extra radioactive materials flying everywhere, but that might not be the only issue, especially when referring to implosion-types, which ensure that the entire ball of fissile material is compressed in all directions. I also cannot find any proof that this is really the case. Just what really prevents the fissile material from undergoing nuclear fission?

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    $\begingroup$ B. Cameron Reed has a series of articles in the American Journal of Physics covering the basics of nuclear physics as understood by the Manhattan Project. One place to start would be American Journal of Physics 88, 565 (2020); doi: 10.1119/10.0001206, one of the more recent ones so you can trace backwards. Figure 1 there is particularly illuminating on this question. $\endgroup$
    – Jon Custer
    Nov 10, 2020 at 14:25
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    $\begingroup$ Statistics (while compressed) of probability of neutrons hitting a nucleus, and yes initial explosive force, once overcoming the compressive forces, scatters stuff everywhere. $\endgroup$ Nov 10, 2020 at 14:29
  • $\begingroup$ "Critical mass" is not a definite number of kilograms. *A* critical mass is an assembly —a mass of nuclear fuel—in which the average number of new fission events triggered by any one fission event is 1. The mass of fuel in a power reactor becomes critical when neutron absorbing "control rods" are withdrawn from it. The mass of fission fuel in a nuclear weapon becomes promptly supercritical when the "core" is compressed by the imploding detonation wave from the high explosive lens assembly. $\endgroup$ Nov 11, 2022 at 21:43

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A detailed answer is probably not appropriate on this stack. (Note that when I posted this answer it was on the world building stack, not the physics stack. On the physics stack a detailed answer would be far better.)

But very briefly, it has to do with efficiency and the speed the thing blows itself apart. The time for burn rate to rise and the time the device starts to explode compete. So the nuclei are flying apart before more than a small portion are used up.

Consider a compression type device, with a shaped charge that compresses a sphere of Plutonium. In some designs there is also a tamper. This is a shell of material around the core that acts to reflect many neutrons back into the core, further reducing the required critical mass.

The characteristic time of increase of burn rate is extremely sensitive to the geometry of the fissile material. If the mass is just below critical at its non-compressed density, then a very small compression puts it over. If it can be put far enough over such that it reaches prompt critical, then the doubling time for energy output is in the range of a few micro seconds.

But recall that the mass only needs to expand a very small amount to fall below criticality again. So, as the energy is released and the explosion starts its very early stages, it does not have to go far to cause the reaction to effectively halt. So if the original chemical explosion only reduced the radius of the core by, say, 1% (not the actual number, but to have a number) then the explosion only has to progress far enough to overcome that 1% to stop the reaction. If the explosion kicks the tamper away, the reaction stops.

There are a bunch of additional effects that would be difficult to calculate. I can't even tell you whether they speed things up or slow them down just off hand. For example, each fission leaves fragments of the original nuclei. Some of those are strong neutron absorbers. There is a temperature effect. Hot nuclei are moving, so it changes the effective energy spectrum for the reaction.

But the dominant effect is competition between the speed of the burn and the speed of the core exploding. If it explodes too quickly you get what is known as a "fizzle."

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As I noted above in the comments, Reed's paper is a wonderful overview of the conditions in a bomb, going back to Serber's Los Alamos Primer. As noted in the introduction to Reed's paper:

One full page of the Primer was devoted to a hand-drawn graph that illustrated the evolution of neutron density, energy density, and pressure within an exploding bomb core as a function of time. While based on an approximate treatment of neutron diffusion for the purpose of informing his audience as to the orders of magnitude they would be dealing with, Serber’s plot still stands as a remarkable example of effective graphical display of information.

Reed repoduces the Serber plot in Figure 1:

enter image description here

Note the tiny bar labeled 'Efficiency' down in the lower right corner, and compare with the pressure and temperature lines, both of which are significantly exceeding the core of the Sun. One does not reach even 1% efficiency until neutron generation #36, and 100% efficiency is reached in neutron generation #41. The trick, of course, is holding it all together long enough to contain the extremes of energy density, temperature, and pressure before flying apart.

A fun quote from near the end of the (short) paper is:

"A density of a few quadrillion neutrons per cubic centimeter sounds fantastic but, in reality, corresponds to fission of less than one part in a million of the 235U contained in any cubic centimeter of the core."

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  • $\begingroup$ Just as a question: how exactly does that diagram work? Is it that those are the conditions at each time, under ideal conditions (because the efficiency goes to 100% after enough time, which is impossible in real life)? So that at, say, even 1% efficiency, we have temperatures of 10 billion (not million!) degrees and pressures over 100 billion atmospheres (10 PPa)? $\endgroup$ Nov 11, 2020 at 4:22
  • $\begingroup$ @The_Sympathizer - the paper describes how the diagram is constructed. $\endgroup$
    – Jon Custer
    Nov 11, 2020 at 21:26

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