... no it... wouldn't? Fission does not work like that. Firstly, if you cut an oxygen atom in half... well, actually, if you cut an oxygen or nitrogen atom in half you actually lose energy and are more likely to cause freezing than explosions, because it's below iron in the periodic table and thus the exothermic reaction is fusion, not fission. Or to put it in simpler terminology: for atoms lighter than iron, it takes energy to split it and you get energy by fusing it. For atoms heavier than iron; vice versa. This is why stars fuse hydrogen into heavier elements, but can't create anything heavier than iron.
This is incorrect. Well, maybe, who actually knows, because a magic sword that somehow cuts atoms is probably doing precisely whatever the fuck it feels like. However, we'll just asume the whole process is vaguely wrapped up in normal physics for the sake of actually being able to have a discussion.
The energy to perform fusion would not be retroactively extracted from the thermal state of the environment, it would be applied by the sword itself to produce the nuclear separation in the first place. Which means instant high energy particle soup, agitated nuclear shells, and all the good stuff(even if we assume the sword is nigh perfectly efficient, a lot of atoms are still going from 'sphere' to 'hemisphere' and that is going to make them
deeply unhappy). I'm not sure how bright this would actually be(How much wood would a wood chuck chuck if a wood chuck could chuck wood?), so I can't say whether it would amount to a microcosm of a nuclear explosion, but there'd probably be a hell of a lot of gamma rays floating about making people miserable.
Gamma rays do many things, but making things colder is generally not one of them.
Secondly, even if you cut one uranium atom in half... nothing happens. Yes, atomic energy is denser than any other form, but atoms are very small. You need to split a great many of them to spark runaway fission or produce any noticeable amount of energy. Cutting air wouldn't do it - you'd have to cut a rod of uranium in half. And frankly, if you have that much uranium in one place, it's close to critical mass anyway.
A sword that swipes through the air and only hits one atom is quite something. Then again, a sword that cuts through nuclear shells is also quite something. Nonsensical hypotheticals get a bit nihilistic if you stare at them too long.
Atoms might be really small, but they are generally so numerous you can rely on them bumping into each other in macroscopically significant quantities. Hence why the word "macroscopic" can even exist in the first place, because atoms actually bump into things quite reliably. Now, the nucleus is a lot smaller than the electrostatic shell, so it'd be hit a lot less often, but there's a hell of a lot of sword, a hell of a lot of air, and there is a hell of a lot of energy in the involved nuclei. So even relatively poor collision conditions are going to produce some pretty staggeringly dangerous results.
And thirdly, fission does not, on its own, explode. The reactors are what explode. Fission itself doesn't give off "explodium energy", it gives off
heat, and since fissionable material does not hold similar properties to petrol or nitroglycerine; there is nothing to explode. A critical fission meltdown is exactly what it says on the tin - the uranium fuel rods
melt down because they're giving off so much heat the metal melts, and then proceed to melt through the bottom of the chamber, flash-convert the coolant into steam (
that is what makes the reactor explode, and the steam cloud scatters radioactive fallout all over the region from bits of irradiated material carried along with it) and then
keeps going. The
slag heap in Chernobyl, somewhere in the basement? It's
still semi-molten, because even thirty years later; enough heat is being produced inside from fission to keep it from solidifying (it's also giving off such high levels of radiation that standing near it for ten minutes will make you very ill, and when it was still hot, five minutes was fatal).
This paragraph is just weird. By that technicality, nothing explodes. An explosion(that is, a pressure differential created by the expansion of a given material in a medium driven by the descent of said to a lower energy metastable state - thus releasing large quantities of work with which to make shit move) is always a secondary effect of a 'more primary' mechanism. Oddly enough though, in nuclear interactions, for once it's not actually temperature. The initial expansion phase of a nuclear event is driven by radiative expansion, in which the hypoethetical thermal flux of the excited medium goes largely unexpressed until the convective stage(which on the timescale of nuclear processes is an age after the actual nuclear reaction). It's still technically there, it's just not relevant, because it can't do anything yet.
More relevantly, in nuclear physics, temperature is more of a byproduct than it is primary energy. Most nuclear energy is derived from shell displacements of various sorts(from outright escapes to nucleons being bumped into unstable orbits), which mostly emit high energy X-rays and stuff when they settle(all sorts of other junk too, but I'm lazy so I'm pretending it's largely absent due to the lack of any sort of conventional instability). Which then go on to get absorbed by something and make
it hot(because it's newfound energy isn't tied up in a peculiar nuclear state that cannot be expressed as thermal flux). Which is where the radiative expansion phase of a nuclear event comes from, the opacity of the air to gamma rays diminishes as it ionises, so as the initial gamma pulse moves through the air, it is absorbed, and makes it hot enough to itself emit gamma rays(which it is now transparent to) and a new layer of gamma ray excited air is produced. This process continues until the energy is dispersed enough the air becomes naturally transparent to the resulting light, you get your initial nuclear flash, eventually(entire milliseconds later IIRC) sonic separation occurs, the fireball's expansion drops below the speed of sound and it is momentarily dimmed by the highly opaque wall of air that just freed itself, the shockfront spreads and turns transparent and the fireball - briefly and counterintuitively reheated by the radiation trapped behind the momentarily opaque shockfront - flashes a second time(albeit vastly less impressively).
What this all essentially means is that you're pretty much right in your conclusion. A magic sword cutting atoms isn't going to look like a nuclear explosion, because nuclear explosions are incredibly bizarre and finicky things that require extraordinarily specific circumstances to occur. Your reasons why however are way off the mark. The sword cutting atoms would, due to all the rebounding nuclear shells and general upset caused by telling an approximate sphere of nucleons it is now a hemisphere(and it attempting to reconfigure back to being spherical, not to mention the cataclysmic energies involved in overestimating the requisite separation energy a smidge) is going to cause a hell of a lot of spontaneous emission of all sorts of nasty junk. Much of which is liable to be photons hard enough to be a vacuum frequency, causing gross incandescence of the blade(plausibly heating the air enough to be actively dangerous to the surroundings, albeit it'd still look nothing like an actual nuclear event, just a really odd fire).
In summary, a nuclear slicing blade is by any even remotely realistic(and boy do I take issues with
that qualifier) description of it's behaviours, going to make a lot of things very hot and very bright. So much so it may well end up setting everybody in the vicinity on fire. It would, however, not be a kaboom. It'd be a perpetually fizzling mega-torch of oh-god-my-face-why. Which probably would make it a great power source. Assuming you could find something that could survive swinging it for long enough to make the process viable.
P.S. A nuclear explosion is rather distinct from something you'd want in a reactor. Just so we're clear here. A nuclear explosion uses supercriticality to induce a runaway nuclear reaction. Nuclear reactors are a long way from supercriticality, because supercriticality versus normal nuclear excitation is rather like the difference between normal combustion and attempting to run your car on C4.
EDIT: Actually, thinking about it. I had so much trouble internalising the hypothetical that it's possible our assumptions about the arbitrary cutting mechanism of the hypothetical blade fundamentally differ. I mean, is it some kind of sub nuclear taper('cutting' doesn't exist at this scale, but hey-ho magic)? Or some kind of arbitrary cutting edge separation mechanism of arbitrary area(because magic)? What is the defined viable collision dimensions at work here considering we're essentially talking about effectively carving apples by hitting them with a mountain range? So all the stuff about heat and light may not be even slightly valid, because there's so many different arbitrations about how it's achieving the separation.
I stand by the "it's not going to make things cold" though.
