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So, this is a question that has been puzzling me for numerous reasons. Be it for advocating nuclear power, or getting a bit of nerd rage when watching a sci-fi work, or having an argument with someone.

Pretty much everyone knows that you need as much U235 you can get in a given concentration of uranium to make a bomb that's feasible and practical since the presence of U238 slows down the reaction. So working that backwards, is there a concentration of U238 to U235 where it's impossible for it to become supercritical because there are too many U238 atoms absorbing the neutrons and thus cannot trigger a nuclear detonation?

I have looked at the wiki for it: https://en.wikipedia.org/wiki/Enriched_uranium#Highly_enriched_uranium_.28HEU.29

If I am reading the second to last sentence on the first paragraph correctly, that would mean any Uranium that is below 5.4 enrichment would be physically incapable of undergoing nuclear detonation regardless of mass of uranium involved. But I'm not sure I am interpreting what they have to say correctly, so I am asking here for further clarification.

Since reactor grade uranium is only 3-4% enriched, that should mean it is impossible for that grade of uranium to ever achieve nuclear detonation, even if you tried. There is also a blurb about this notion (fact?) in this Chernobyl footage, but given it's age, and lack of explanation as to why, I'm not sure this is a valid source. https://youtu.be/Cc-vvhWXL9Q?t=14m50s

So, if I got all my duck in a row and understanding this correctly, assuming 3-4% enriched uranium is being used, would it be accurate to say that nuclear reactors (Of the above parameters), cannot, and won't ever explode in the sense of an atom bomb?

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Yes, nuclear grade uranium can never explode in the sense of an atom bomb for various reasons
1) Only Uranium 235 is capable of sustaining nuclear chain reactions and as you said reactor grade uranium has only 3-4% of that whereas the bomb dropped on Hiroshima had well over 80%
2) Critical Mass : The term simply means that there's enough fissile material present to sustain a chain reaction, and a supercritical mass is where enough material is present for the fission rate to increase.
A nuclear weapon is designed to release all its energy in one incredibly destructive blast, which means the material wants to be as densely packed with fissile material as possible in a homogeneous sphere(nearly)
Whereas reactor cores are meant to produce a steady, controlled release of energy, and even the sort of energy buildup needed to produce a meltdown can't ever attain the speed and intensity needed for an explosive nuclear energy release. The geometric arrangement of uranium-235 in a nuclear reactor is just fundamentally not conducive to the spherical arrangement needed for an explosive chain reaction, and the amount of non-fissile uranium-238 in reactor-grade uranium also stops any runaway reactions.

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To add to Prabhdeep Singh's correct answer, there's another fundamental reason why a reactor would never explode like a bomb even if using highly enriched uranium. And that is simply that an exploding critical mass is, well, exploding, so it's dispersing and thus quenching the reaction. Moreover, temperature rises also tend to quench the reaction. Critical masses, unless very carefully designed, don't tend to make big nuclear explosions: they tend to blow themselves apart.

If you must make a bomb, then you must design things so that the fissile material stays together in a supercritical mass long enough for a sizeable fraction of it to undergo fusion. In an implosion-type fission weapon, one must set up a huge acoustic spherical wave that crushes the fissile material perfectly symmetrically so that the ingoing momentum of the material keeps it together long enough before explosive reaction quenching puts an end to the whole process.

There have been some famous accidents where critical masses of U235 have been accidentally assembled with gruesome outcomes, but none of these outcomes was an explosion. See my answer here for more details.

Of course, a nuclear reactor releases a huge amount of heat, so, whilst it cannot end in a nuclear explosion, if the operators lose control of the reaction the sheer heat output can lead to catastrophic explosions (usually from flash vaporization of water, as happenned at Chernobyl) or destruction of the plant and escape of radioactive material.

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    $\begingroup$ I always end up in the Wikipedia rabbit hole when I start reading about nuclear accidents. But the one I find most fascinating is the screwdriver slip at LANL. $\endgroup$ – tpg2114 Mar 7 '17 at 12:49
  • $\begingroup$ @tpg2114 That's the infamous Louis Slotin one that I mention in my other answer. $\endgroup$ – WetSavannaAnimal Mar 7 '17 at 21:19

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