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What would happen if the Earth's inner core suddenly changed to unprocessed, natural uranium without the volume of the core changing? How soon would we notice any changes? What would be the implications?

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    $\begingroup$ Would the core stay the same volume as it is now, in which case everything would feel massively heavier, or would it stay the same mass, in which case everything would experience a very rapid sinking sensation? $\endgroup$ – Joel Harmon Sep 27 '16 at 15:10
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    $\begingroup$ Are you asking about depleted uranium, natural uranium, enriched uranium? You should specify the isotope(s) as it will likely make a big difference in the answers. $\endgroup$ – James Sep 27 '16 at 15:15
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    $\begingroup$ The isotope is certainly relevant, but on the scale of a planetary core a "representative sample" of uranium unrefined would certainly be supercritical. $\endgroup$ – SudoSedWinifred Sep 27 '16 at 15:59
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    $\begingroup$ What if the clouds suddenly turn into marshmallow?? What if all rabbits turn upside down???? Such interesting questions, please give scientifically accurate answers. $\endgroup$ – pipe Sep 27 '16 at 18:38
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    $\begingroup$ To the others with moderation power: Why would you put this question on hold? "Good answers would be too long for this format" is demonstrably false since by the time the question was on hold I had already provided a good answer. Please restrain the use of your forum privileges in favor of more free discourse. $\endgroup$ – kingledion Sep 28 '16 at 0:56
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TL;DR: The Earth becomes an expanding ball of (highly radioactive) plasma

First let me preface this by saying: I'm not going to do links like I normally do. The physics covers a lot of ground and this is just a summary, if you want details and equations they are available on Wikipedia, and elsewhere. I italicized some key phrases you can Google search, if you are interested.

Fission and Fissile materials

Uranium is used to make both bombs and power plants. It creates energy though the process of nuclear fission, where a Uranium atom interacts with and absorbs a neutron, and then splits into two fission products, converting rest mass into energy, and distributing that energy into neutrinos and gamma radiation. Occasional, another small particle is produced, like a helium or tritium nucleus.

Many atoms are fissionable: able to undergo a fission reaction. There are two broad categories of fission: fast and slow reactions. These refer to the energy of the absorbed neutron that causes fission. A fast fission reaction means the isotope must absorb a high energy neutron to undergo fission. Uranium-238 is an example of an isotope that undergoes fast fission. Fast fission works well in bombs.

For all fission reactions, the neutrons that are released in the fission process are fast. Therefore, for a slow reaction to happen, the neutrons must be slowed down or 'thermalized'. Generally, this is the preferred method in nuclear power, since thermalizing the neutrons also transfers heat energy out of the fission products and into some medium. Common thermalizing mediums include water and graphite. Hydrogen atoms as part of a molecule are good at thermalizing, so both water and hydrocarbons are good moderators.

Fissile materials are a subset of fissionable materials that can undergo a fission chain reaction; that is, where the byproducts of one fission reaction will start another. The effective neutron multiplication factor (k) is a term for the ratio of neutrons from one 'generation' to the next. If the number is greater than 1, then the number of neutrons created by a set of fission reactions will be greater than the number of neutrons it took to start that set of reactions. For example, if k = 1.1, and there are 100 fission reactions, then the neutrons from those reactions will cause 110 fissions, and those fissions will cause 121 fission, etc until all fissile material is either consumed or blown apart.

Uranium-235 and Plutonium-239 are the two most common fissile materials. Uranium-235 is present in nature, while Plutonium-239 must be created. The most common isotope of Uranium is U-238, which is not fissile. U-238 undergoes fast fission, but the neutrons released in the fission reaction are of a slightly lower energy than is required for fission; therefore no chain reaction can propagate through U-238. However, if U-238 interacts with a thermalized neutron, it can absorb that neutron, creating U-239. U-239 is unstable, and will beta decay twice with a half-life of days into Pu-239. This is how Pu-239 is formed in a breeder reactor. U-238 is thus referred to as a fertile material since it can be changed into a fissile material in a breeder reactor.

Critical Mass

A sufficiently dense object composed of fissile material may achieve critical mass and begin to undergo fission. For pure Uranium-235 this will occur with a 8.5cm radius sphere of mass 52kg. This is how the first atomic bomb was made; Little Boy was a 'gun'-type bomb where two hemispheres of uranium, each below critical mass, are shot together with explosives. As they approach, the bomb reaches critical mass and a fission chain reaction occurs.

Critical mass affects k because of the concept of neutron leakage. In U-235, each fission reaction creates more than two neturons on average, so in an infinitely large region of U-235, k is much larger than 1 and fission happens quickly. However, in practical applications (bombs and powerplants) there are a few tens or hundreds of kilos of U-235. This means that neutrons, especially the high energy 'fast' neutrons tend to 'leak' out of the reacting core. This leakage is usually the biggest cause of loss of neutrons from one generation to the next. Below critical mass, leakage is so significant that k is below one, and no chain reaction can occur. Above critical mass (or supercritical) the chain reaction occurs.

In general, bombs operate by compressing (often using conventional explosives) as much uranium into as small an area as possible. Once this hits critical mass, the reaction is sustained and temperature increases, which tends to blow the uranium apart so that the reaction goes subcritical. The challenge of bomb-making is to organize the pressure changes caused by fission so that most of the uranium is consumed in fission before all the parts are blown to kingdom come. This is hard, and that is why you hear about things like North Korea's bombs 'fizzling.' This means they blew apart before all uranium could fission.

On the other hand, criticality is a critical (so punny!) concept in nuclear power. A safe reactor maintains k = 1; exactly critical at almost all times. If k > 1, then the reactor is supercritical, and power is increasing. This is good if you want more power, but if k >> 1 then your power plant becomes a bomb. American reactors (especially the pressurized water reactors that I am familiar with) have various engineering factors that make it nearly impossible for a runaway chain reaction. The Soviet RBMK reactors like Chernobyl...not so much.

What would happen to a uranium ball the size of the earth's core

As you may have noticed, U-235 can spontaneously start a chain reaction if it is concentrated above its critical mass. While U-235 is only 0.72% of Uranium by mass, there is enough in a ball the size of the earth's core to be supercritical. The important point is that leakage is effectively zero; a fission event near more than a kilometer from the surface of the uranium sphere has basically no chance of escaping. Thus, each neutron that forms is likely to find another U-235 eventually.This has happened before in our planets history, in a natural nuclear fission reactor at Oklo, Gabon.

Since U-238 is a breeder, many of the neutrons generated from the U-235 chain reaction would be absorbed in U-238 forming Pu-239, thus adding more fuel to the fire.

A planet would never form a core of uranium, since fission would occur while still as a gravitationally affected proto-planetary cloud. But supposing an evil Worldbuilding wizard turned the Earth's core to Uranium, the core would then undergo a fission chain reaction and vaporize itself in the amount of time it takes for a neutron to travel from one side of the core to the other (about 10 minutes).

This would compound the problem. Some fission by products like Iodine can poison a nuclear reaction by absorbing excess neutrons. However, once the whole planet vaporized, the heavier elements would be pulled by gravity to the center, while fission by-products like iodine would float to the top. Thus the heaviest elements (Uranium and Plutonium would be the heaviest two present) would sink to the center, concentrating themselves and perpetuating the chain reaction over the course of days and weeks, generating more and more energy.

Brief math foray at the end: 1kg of Uranium (or Plutonium) undergoing fission releases about 24 GW-hours of energy, or 86.4 TJ. If the core is a sphere of 1200km radius; then it is composed of 1.4e26 kg of Uranium. The energy released by this reaction is 1.2e40 J. In fact, there will be even more energy from the radioactive decay chains of various fission products. This is a simplistic calculation, but since this energy is eight orders of magnitude greater than the gravitational binding energy of earth, I conclude that before all the uranium is consumed, the Earth will have been converted to an expanding ball of plasma.


Edit for more science and accuracy:

Some commentators questioned the ability of the un-enriched uranium ball to sustain a fission chain reaction. I offer two reasons to think that it will.

Firstly, there is the concept of the neutron cross-section of absorption. Neutron interactions with atoms happen on a quantum scale, so a neutron-nucleus interaction isn't as simple as trying to hit a basketball with a tennis ball (as you might think using classical physics). Specifically, the cross section for interaction of an atom is different depending on the particle that is trying to interact with it. This chart has some thermal neutron cross sections listed on it. Specifically the radiative capture (absorption of a neutron and emission of a gamma particle) cross section for U-238 is about 2.7, while the radiative capture cross section of U-235 is 99 and the fission cross section of U-235 is about 583. That mans that a neutron approaching U-235 is $\frac{583}{2.7} = 253$ times more likely to interact with U-235 than U-238. Thus, although U-238 may be much more prevalent (and it is, the ratio is 138:1 U-238:U-235) a neutron passing through an infinite volume of natural Uranium will have a 35% chance of being absorbed by a U-238, a 9% chance of being absorbed by U-235 and not causing fission, and a 55% chance of being absorbed by U-235 and causing another fission.

So far it looks like the chain reaction will go on swimmingly. However, there is still one important factor of the neutron life cycle: resonance escape probability (p). Resonance bands are energy levels where certain atoms have an increased affinity for neutron absorption. For U-238, there are a series of resonance bands between 6eV and 200eV. For a normal reactor p might be between 0.75 and 0.85. Thus the $k_{eff}$, or effective multiplication factor is $$k_{eff} = \left(\text{number of neutrons per fission}\right)\cdot\left(\text{chance of neutron being absorbed in fuel an causing fission}\right)\cdot\left(\text{chance of neutron not being abosrbed in resonance region}\right)$$ $$k_{eff} = (2.43)(0.55)(0.8) = 1.07,$$ which is supercritical. This is the calculation I initially performed.

However, the assumption of $p = 0.8$ is probably bad for a solid block of Uranium, for two reasons: Uranium is a poor moderator so the slowing down length of neutrons is larger here than in a water-moderated reactor. A longer slowing down length means more opportunities to interact with and be absorbed in a resonance region. Secondly, a reactor has many materials other than pure uranium to interact with; specifically oxygen since uranium fuel is in the form UO$_2$. I just don't know what p should be, but it probably should be less than 0.8. If it is less than ~0.75, then the core is no longer supercritical.

However, this brings up my second point. Since there is no leakage, there are only three possible outcomes for a neutron, as discussed above: a 55% chance of starting a fission, a 35% chance of turning U-238 into U-239, and a 9% chance of turning U-235 into U-236. U-236 is not particularly interesting, since it does not have a large cross section of absorption. It is a long-lived radioactive waste. U-239 is much more interesting because within a few days it will become Pu-239, which is fissile.

Supposing a chain reaction does not start immediately, it will only be because a great number of U-238 atoms are being converted into Pu-239. After a couple of days, there will be a large increase in Pu-239, which has an even larger cross section for neutron absorption than U-235. It won't take a large increase in Pu-239 before the chain reaction can start.

I don't have the data to definitively say if the chain reaction will start immediately or if it would wait a few days until sufficient Pu-239 was formed, but rest assured, the end result is the same as in my TL;DR summary.

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    $\begingroup$ The most critical error in this answer is the claim that "each neutron that forms is likely to find another U-235 eventually." No, neutrons would be far more likely to encounter U-238. I doubt that such an assembly would be supercritical. The natural nuclear reactor happened at a point in history when the concentration of U-235 was higher, estimated to be 3.1%. I suspect the majority of the heat generation in such an object would come from ordinary radioactive decay (U-235 -> Th-231 -> Pa-231 -> etc.) $\endgroup$ – Dietrich Epp Sep 27 '16 at 17:50
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    $\begingroup$ @DietrichEpp... What error... it's a 1200km ball of Uranium, you have no idea what isotopes it's predominantly made of. It was placed there by an evil wizard. It's highly likely that each neutron will instantly run into another U-235 in this situation for all we know... There is no 'historical' precedent. $\endgroup$ – Ryan Sep 27 '16 at 18:02
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    $\begingroup$ It sounds like you're assuming that it is enriched uranium. As for "historical" precedents, uranium is a naturally occurring element and we have historical precedents for working with it. $\endgroup$ – Dietrich Epp Sep 27 '16 at 18:11
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    $\begingroup$ I agree with Dietrich. Natural Uranium is over 99% U-238. Since the OP asked about the core being converted to "unprocessed, natural Uranium", one has to assume any free neutron would almost certainly end up encountering a U-238 rather than a U-235 atom. To enrich it, it has to be processed to bring up the concentration of U-235 from under 1% to over 20%. Even if you brought it up to 3%, you might end up with a natural reactor, but at less than 1%, I can't see that. $\endgroup$ – user11864 Sep 27 '16 at 18:24
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    $\begingroup$ This is a trivial pop culture comment. The 1949 version of Superman's origin story it was explained that the planet Krypton had a uranium core. While this does explain satisfactorily why Krypton exploded, what it doesn't explain is why & how Krypton survived long enough for humanoid Kryptonians to evolve & develop a civilization. As your answer shows planets with uranium cores won't last long. Loved your answer & gave it plus one. $\endgroup$ – a4android Sep 28 '16 at 2:10
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Uranium is a poor electrical conductor, so disregarding anything else, if the current Iron Core would be replaced by Uranium, the first thing people would notice would be the Sun, or, more particularly, sunburn!

Why, well, you see, you've just changed the state of the electromagnet that is the Earth. The Iron that used to generate a huge electromagnetic field that protected the Earth from the Solar winds no longer operate, meaning Earth's atmosphere is being stripped away a-la Mars.

Within a few days the entire Earth would become sterilized and desolate and any and all life would cease to exist. (Let's face it, the only place that might be safe is deep underground in nuclear bunkers, but as this change was instant and without warning, nobody would be in those said bunkers.)

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    $\begingroup$ And since uranium is a lot denser than iron, the earth would spin at a faster rate. $\endgroup$ – user10945 Sep 27 '16 at 15:31
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    $\begingroup$ @MolbOrg I can't imagine anyone in their right mind thinks there is life currently on Mars. The question isn't "is life there now" it's more "was life ever there or could there ever be life later (as in us)." $\endgroup$ – Virusbomb Sep 27 '16 at 16:11
  • $\begingroup$ @Virusbomb mars.nasa.gov/programmissions/science/goal1 I cite: NASA will also look for life on Mars by searching for telltale markers, or biosignatures, of current and past life. $\endgroup$ – MolbOrg Sep 27 '16 at 18:31
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    $\begingroup$ Wrong, see here worldbuilding.stackexchange.com/questions/56791/… $\endgroup$ – Karl Sep 27 '16 at 20:42
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    $\begingroup$ it will take millions of years, and that is not even close to any definition of rapidly which we as humanity used to. $\endgroup$ – MolbOrg Sep 28 '16 at 15:32

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