Suppose we used SCP-261, the vending machine that produces anything, and ask for a cup of neutron star. The machine instantaneously produces this.
Suppose also that the vending machine is located at a normal office building, not some underground lair or the like.
What effect would this have, and how much damage would it do? Would it kill everyone in the building? Destroy the Earth? Surprisingly very little effect?
This is more or less my best guess.
We're talking about a mass of about one hundred billion tons, composed of neutrons, previously held together by a terrifying gravitational field - and now unleashed.
The cup starts falling down under the Earth's gravitational attraction, but at the same time it explodes outward (so, also downward) with a velocity equivalent of a 2-3 MeV energy (so, 20000-30000 km/s). This makes the actual fall negligible; we may consider the cup at rest in respect to the Earth (actually, after just one microsecond, there no longer is a cup - there's a spheroidal mass of neutrons roughly twenty meters in radius, at a temperature equivalent of at least several million Kelvin, exploding outwards at a measurable fraction of the speed of light).
The energy release is immense (this other answer would place it at around $1.5\times10^{28}$ J, or almost forty thousand times larger than the Chicxulub dinosaur killer) and we may divide it, initially, into two parts:
From one third to half of the total energy escapes upward almost harmlessly, another fraction is probably ghosted away by fleeing neutrinos, but that is far, far from being enough.
Neutron flux of a sufficient density activates aluminum silicates that make up most of the Earth's superficial crust: within a small radius, there are enough neutrons to ensure the triple-capture activation of 28Si to 31Si. Some of that will be made less harmful by a fourth capture, that extends its half-life from two hours and a half to one century and a half. Aluminum activation transforms aluminum into silicon, releasing a considerable amount of energy as heat and gamma rays.
Communications are instantly obliterated on a vast area by both the EMP release (which also fries most overhead satellites) and the Heaveside layer being reduced to tatters.
Within seconds to minutes, the pressure release from the crater area will have caused a second, less flashy but even (on the long run) deadlier supervolcano explosion, as the mantle magma outgasses a pressure equivalent to at least 10-15 kilometers of rock. The explosion drives through the incandescent and radioactive gases, dust and rubble, mixing with them and increasing the firestorm. An inordinate amount of radioactive ashes and noxious gases is released into the atmosphere.
(Hal Clement's first published story, Proof, deals with more or less this very scenario - a whole ship made up of neutronium, colliding with Earth. The neutronium of the story, though, is cohesive, non-radioactive and simply very hot and dense, so the impact results only in a vast lava lake).
Within minutes, the neutrons still at large start undergoing beta decay. A sizeable volume of the Solar System gets gamma irradiated.
Radioactive tephra start reentering the upper atmosphere, while the radioactive cloud reaches the stratosphere and begins diffusing.
Also, earthquakes complete the destruction of mostly everything in a 500-1000 kilometer radius. The shock is enough to trigger most faults in the area. Depending on where the apportation happens, secondary phenomena may occur; in the U.S. we might be looking at activations of anything from Yellowstone to the San Andreas fault to the Juan de Fuca structure.
Between ten and twenty minutes later, give or take, the seismic wavetrain hits the opposite half of the globe, triggering secondary earthquakes.
Within hours, the sky becomes red and the infrared emission alone triggers a worldwide firestorm, the smoke enough to blot out the Sun.
Some days later, the radioactive dust starts further dimming the sunlight almost everywhere and atmospheric water vapour starts condensing; the torrential waterfalls are initially radioactive only in the impact area, but will become so more or less everywhere within a few weeks.
The massive (and ongoing) heat release disrupts weather patterns throughout the globe, the increase in temperature enough to siphon oxygen out of the seas into the atmosphere, where fires and decay processes will take care of it.
Mostly everybody dies. Prepared people, with lots of resources, die anywhere between one week and five years later. A nuclear-powered, well protected arcology might remain viable for an indefinite time; anything else probably won't.
Asking for a chocolate would have been a whole sight better.
UPDATES: good news from the SCP Foundation
Further analyses indicate that is unlikely for SCP-261 to materialize a cupful of neutronium. SCP-261 has only ever supplied snacks or something that someone, somewhere might have considered a snack; the most dangerous apportation recorded was that of one item of SCP-417, which is theoretically edible.
Neutronium, on the other hand, is unlikely to be edible by any being capable of interacting with SCP-261 at all, so it is equally unlikely that SCP-261 might accidentally destroy the human race.
Moreover, in all cases the apported object was packaged in something capable of maintaining the contents in a stable state (in some cases, keeping it alive until it could be consumed), however unlikely that might have seemed. If SCP-261 materialized the requested object as usual, the resulting apportation would then be a staggering amount of mass, within an enclosure capable of stabilizing hot neutronium. Such an enclosure would have no problems in withstanding the comparably negligible hardships of immediately sinking towards the molten center of the Earth. An explosion at that point, while possibly damaging worldwide, would yet not be, pardon the pun, of Earth-shattering proportions. It is still likely that the materialization and sinking would have enough side-effects to kill everyone in the room, possibly in the whole building.
The answer isn't entirely clear what the final state of the Neutron Star matter would be, but it would most definitely completely destroy the "Totally Normal Office Building", and most of the country... and probably most life on Earth.
See this related question: https://physics.stackexchange.com/questions/10052/what-would-happen-to-a-teaspoon-of-neutron-star-material-if-released-on-earth
Edit: The gravitational binding energy of Earth is 2e32 Joules and the energy released in this event is approximately 7.5e28 Joules... so Earth will not be "destroyed". A quick calculation of the energy required to vaporize the oceans is 3.7e27 J ( 1.4e21 kg water * 100 C * 4200 J/kg specific heat, then vaporized at 2260 kJ/kg heat of vaporization). It is safe to say a decent portion of the oceans will be boiled away.
According to the answers to the Physics question linked by abestrange this would result in the Earth being hit by 250 million tonnes of neutrons travelling at .1c+. I feel confident this would turn everything above horizon radioactive including significant portion of the ground beneath. Neutron scattering would extend this beyond the horizon too.
Bulk of the energy would then transform into heat creating a huge fire storm that lifts much of the irradiated material into stratosphere. Gravity will then bring it down "somewhere". Normally you'd have to start thinking about wind patterns and the amount of debris but in this case I think we can just assume the entire surface of the Earth comes covered by radioactive crap.
Which is a good thing because once it is down it is no longer stopping sunlight.
Just noticed that the amount in this question is much larger than the one in the physics question but frankly it doesn't really matter, does it? Only real change is that the extra energy removes all need you might have had to worry about the fallout coverage.
So "everybody dies"? Although people who still have nuclear fallout shelters and are far enough will have time to take cover. Not sure how survivable that actually is. I think they were mostly intended to protect people when the city they are in gets blasted not to support populations when the entire surface is irradiated.
EDIT: I guess I must reconsider this. On second thought the explosion would be powerful enough to cause a shock wave that causes powerful earth quakes world wide. And the ionizing radiation would cause an EMP. So evacuation to shelters probably would not be possible. People would probably just have time to get confused about what is going on before everything starts shaking and collapsing.
Neutron star matter weighs about a mountain per teaspoonful. So much that if I had a piece of it here and let it go I could hardly prevent it from falling. It would effortlessly pass through the Earth like a knife through warm butter. It would carve a hole for itself completely through the Earth emerging out the other side perhaps in China. The people there might be walking along when a tiny lump of neutron star matter comes booming out of the ground and then falls back again.
The incident might make an agreeable break in the routine of the day. The neutron star matter, pulled back by the Earth's gravity would plunge again through the Earth eventually punching hundreds of thousands of holes before friction with the interior of our planet stopped the motion. By the time it's at rest at the center of the Earth the inside of our world would look a little bit like Swiss cheese.
– Carl Sagan, Cosmos : A Personal Voyage, s01e09, The Lives of the Stars
I'm going to assume we get a cup-a-neutron, which is pre-packaged in a thin-walled container that can maintain neutronium. This material would be far stranger than neutronium, as the only known process that can maintain neutronium in our galaxy is the gravity of a neutron star.
But in theory, a ridiculously strong and indestructible material could put enough pressure on the neutronium to keep it in its state.
Opening it would be a bad idea, but nobody will have time to do that. The single cup will weigh enough that it will penetrate through anything.
The density of neutronium is 4*10^17 kg/m^3. A cup is about 250 ml, and a it takes 1000 liters to make up a m^3; so a cup is nicely 10^14 kg.
The surface gravity of the cup is about 138670 Gs, or 1362009 m/s2.
This is about 1/3 of the surface gravity of an entire white dwarf star. So it won't collect electron degenerate matter, but ...
At a distance of about 25 m, it would generate 1 gravity of acceleration. So even if it was hovering, the office building it is contained within would crunch inward; few buildings are designed to support a full gravity at 90 degrees to vertical.
But it won't be hovering. It will be falling.
It falls at 9.8 m/s2. Things fall towards it much faster; no chemical bond is going to be able to resist the gravity it produces at short range. So it will be falling in a ball of plasma. The plasma in turn will undergo nuclear fusion as its density skyrockets; at 1/3 electron degeneracy gravity levels, light nuclei aren't going to be able to stay apart. Or maybe not; white dwarf stars nova after they accumulate a certain amount of matter.
As it falls it burrows a hole through the planet. If we assume 0.1% total conversion of a path 3 m wide and a density of 5 g/cm^3 via fusion, that produces 141 kg of energy per meter traveled.
By the time the cup has reached the center of the Earth, it'll have gathered up 6 * 1021 J of energy.
But it will also have induced fusion that produces 900 million kg of energy, which is 7 * 1025 J of energy.
So the fusion reaction -- matter being attracted to the cup-o-neutronium and fusing due to the crazy gravity and pressure -- will make the gravitational accelleration from the Earth a rounding error. The cup-o-neutronium will halt before reaching the center of the planet and bounce around within the mantle like popcorn on a plate. I could even believe it will jet itself out of the crust sometimes, and even escape the Earth's gravitational pull.
We'd better hope it does -- if it doesn't, it will turn Earth into a strange star, fueled by the gravitational powered fusion at its core.
The energy required to make the cup-o-neutronium reach escape velocity is 1/2 * (11.2 km/s)2 * 1014 kg, or about 6*1021 Joules
That is bad news. The process that shoots the cup-o-neutron out of the planet is 1000 times greater than a dinosaur killer. Our best bet is that the neutronium falls into the planet, does a pile of insane damage inside the planet (causing massive earthquakes all over earth), then gets shot out of the planet depositing a tiny fraction of its energy on the surface. That seems implausible.
So even if the cup of neutronium was contained in an unobtanium alloy cup that kept it from exploding or the insane amounts of radiation neutronium emits passively from frying everything, the mere existence of a cup of matter that dense would be enough to make Chicxulub look like a dent.
This question has been answered by our lord and savior, Randall Munroe in his book What If?: Serious Scientific Answers to Absurd Hypothetical Questions, chapter "Neutron Bullet".
This chapter is one of the bonus questions only released in the book. Relevant Excerpts have been pasted here.
A bullet with the density of a neutron star would weigh about as much as the empire state building
A bullet is about (9 mm circumference, 19mm long, volume of a cylinder is (pi)(r2)h, π*(4.52)*19 or 1200 millimeters3. A the volume of a cup is 236588 mm3 or around 200 times that of a bullet. Ergo, a cup of a neutron star matter would weigh 200 empire state buildings, give or take an order of magnitude.
If you take neutron star material outside of the crushing gravity well where it's normally found, it will re-expand into superhot normal matter with an outpouring of energy more powerful than any nuclear weapon.
This would be bad, but assuming it didn't expand then...
Whether we fired it from a gun or not, the bullet would fall straight through the ground, punching through the crust as if the rock were wet tissue paper
If you google for "density of neutron star in kg/cm3, you get an example of one that reaches 7 x 1014 grams per cc. A 200 ml cup would have 1.4 x 1014 kilograms of mass.
Let me rephrase without exponentiation. It would have a mass of 140,000,000,000,000 kilograms.
For comparison, the mass of the Earth is close to 6 x 1024 kg. That is 10 billion times more massive than your cup, but at a density that is closer to 5.5 grams per cc.
Anyway, back to the office. The cup will fall from the machine and rip a hole as it sinks to the core of the Earth, displacing crust and exposing a bit of mantle in the way. The people and things closer to it will be torn apart and pulled along it due to its gravity - it may be a ten-billionth as massive as the Earth but you are 6,400 km closer to its center of mass.
Throughout the Earth, powerful tectonic shockwaves cross the planet a couple or more times. The Planet will wobble a bit as its center of gravity readjusts. Earth will be slightly more massive, so its gravity will be stronger - but not enough for us to perceive.
The only lasting effect noticeable by us is that the orbital period of the Moon will be shortened by a few milisseconds. Oh, and the mega crater at wherever the office with the vending machine was located.
ADD: The exposition below was based on a mistaken reading. I got my neutronium mass figure as 100 million tons, misreading 100 BILLION tons is the mass. That makes 1000x, and 10x BIGGER for the asteroid eqivalent - MORE than the 400 km strike Sleep modeled. The correction conclusion is "EVERYBODY Dies", literally, meaning ALL forms of life, period, with a sizeable portion of the Earth's crust and upper mantle ripped off and thrown into space, a murderous wound that might even try to bleed core iron!
But still, just to leave it here - just remember everything must be scaled UP according to the appropriate factors and scaling laws...!
Ahh yes ... a nice little explosionological problem and the answer is - to borrow from Dave Consiglio of Quora fame, "Everybody Dies(TM)" - including virtually all microbial life.
The top answer here doesn't quite do this one justice. It is pretty much the end of at at least most forms of life on Earth, complete and total.
We can roughstimate the energy released by deconfinement of neutron star material with its gravitational binding energy, since that is the force that would otherwise be holding it, and more crucially, the amount by which its energy will be raised, and thus now able to explode with, when it is lifted out of the neutron star by the machine's magic. The energy fraction is about 20% of the mass energy (cite: https://physics.stackexchange.com/questions/195951/what-is-the-binding-energy-of-a-neutron-star). With 100 million tons - which we can make to 100 million megagrams as the famous and aggravating ambiguity of whether a "ton" here is a "tonne" (megagram), US ton, or long ton is a relatively pointless 10% of energy difference at this scale - we can get that the released energy by good ole' $E = mc^2$, times 0.2, is about 1800 yottajoules (YJ).
For comparison, the Chicuxlub impactor was roughly 0.5 YJ, and the TZAR, the biggest bomb humans have built, was only about $2 \times 10^{-7}$ YJ. That means this is 3600 times the released energy for Chicxulub. We can, fortunately, thus using that kinetic energy is proportionate to mass and hence by positing a constant "specific whupass" of as asteroid at a given speed, we can relate this to asteroidal dimensions by saying the effects of this will be roughly comparable to an asteroid 3600 times larger and so heaver than Chicxulub. By the fact that radius, hence diameter, scales with the cube root of volume from geometry, and that Chicxulub was about 10 km in diameter, we can say this is about equivalent to an asteroid strike of 150 km diameter, at the asme speed which we're assuming is relatively typical of asteroids.
What would that do? Well, this type of asteroid strike, while it has never occurred at any point within familiar geological history, is of a kind that may have occurred during the genesis period of the Earth - the Hadean eon (from the formation of Earth at 4.55 billion years / 143 petaseconds ago to 4.00 billion years / 126 petaseconds ago), particularly the Late Heavy Bombardment period.
There was a documentary series that aired around 2003, I believe, that showed research on and a mockup of what an impact of the size of some of these Hadean era impactors would do were it transposed to the modern Earth today, though this one was even larger at 400 km diameter. The series was a joint production both by Canada and Japan (CBC and NHK, respectively) called "Miracle Planet" and "Great Story of 4.6 Billion Years of Earth's Evolution" (Chikyuu dai shinka, 46 okunen monogatari) in respectively English and Japanese and the source of the research for this particular part was a paper by Norman J. Sleep, a planetary scientist at NASA (I believe). He called impacts above a certain size (I think 100 km) a "JUMBO" impactor, and suggested these "jumbo" impacts had occurred not one, but several, times during that period. His thesis was actually more regarding the possibility of survival of life - albeit, very simple life - through such a jumbo strike.
The effects of a jumbo impact are, as said, virtually life exterminating: we could consider this on the smaller size, so some of the effects will be moderated from what was simulated, but not much.
The differences insofar as neutrons vs. asteroids will be chiefly in the beginning. Roughly, as per the current top answer, what will happen is the neutron material will deconfine within micro or even nano-seconds, rapidly developing as it meshes with the surrounding matter into a ball of furiously hot plasma at about a billion kelvins. Half of this sphere will go downward, half upward, in terms of energy. The upward part will effectively be lost to space since the atmosphere, much less the building, are an irrelevant wisp at this scale, so effectively we're actually only left with 1/2 the energy going downward and thus this is not necessarily quite as efficient as an asteroid strike of 150 km - by the same scaling laws, we should try about 120 km instead, so still barely in the jumbo range, but at the low end. The downward part will excavate a crater. From impact studies, there is a general rule of thumb that about a 1/4 to 1/3 root law is followed for crater diameter versus explosive energy release - 1/3 is better for impacts (which are, as said, more efficient at transferring energy), 1/4 for explosions: this is an explosion, but we've effectively already accounted for the inefficiency as just said. Effectively, this means the crater scales the same as impactor diameter, and we can estimate that the resulting crater will thus be 12 times wider than the Chicxulub crater, or 1800 km in diameter. This is comparable to the size of Hellas Basin on Mars.
The basic effect of this worth considering will be the production of a very large amount of rock vapor. The vaporization of rock will extend far into the planetary mantle - simply talking about "making a volcano" is not enough. The "ejecta" from this kind of impact isn't just debris - far more is the vapor plume generated. Insofar as ordinary crustal debris, at this scale the explosion effectively simply peels the crust like skinning a fruit, and then it rains down all around - huge chunks of rock and debris themselves the size of rather modest asteroids coming down everywhere all over, heating up the surrounding crust red hot for maybe another 1000 km about the crater area.
Within the crater, mantle material will uprush as said, but it will now if not vaporized be boiling hot, upwelling and turning out the rock vapor into a huge dome (at least that's how the mockup showed it, though I suspect the actual dynamics will be more complicated and some doubtless reaches escape velocity meaning the Earth loses some mass and don't remember what was said in Sleep's paper regarding this.). Temperature of the rock vapor will be around 4000 degrees C (~4300 K). This is the temperature at which most of the damage will be done. The vapor effectively eventually will spread to form a "second atmosphere" now of very hot rock vapor. The whole surface effectively becomes an over hotter than a blast furnace at this 4000 C temperature. From space, the Earth shines like a tiny sun (this, sadly, the mockup did not do justice to). No humans or any other life form that is exposed, survives. The ocean will rapidly begin to boil off, or better, it gets "ablated" by the vapor cloud above it as it absorbs the infrared radiation (there's a calculation in the paper talking about this that I do remember) within the topmost layer and flies off. Effects from neutronization, decay and activation are completely irrelevant. Radiation doesn't kill you faster than 4000 degree hot blast wind traveling likely much faster than the speed of sound.
At this size, since it's smaller than the 400 km case considered, would produce considerably less rock vapor, but no cooler, so I would estimate that the effect is effectively roughly to shorten the duration due to a thinner vapor cloud. The whole ocean may not boil (keep in mind the vapor cloud is losing energy to space as well), but once the rock vapor begins to condense it starts to rain liquid rock (or volcanic-like glass) down onto the surface and remaining ocean, effectively smothering the bottom and any life that may have held out down there in a layer of rock and pumice.
Insofar as human survival - the answer is pretty much a clear "No", at least not under the parameters of this scenario. Death toll is the entire human species in that regard, essentially by being cremated alive way better than the best crematorium oven can do (maybe only around 1000 C or so). The astronauts on the ISS wouldn't even make it, even to starvation and even if on the opposite side of the planet at the time of impact: the rock vapor cloud and debris would likely be much higher in thickness than the space station's orbit and even if not, thermal radiation at 4000 C vaporizes it like a bug in a bonfire. The only way a human could survive would be to effectively do what Sleep posited as the mechanism for how primitive life might have survived: burrow deep enough into the crust so as not to notice the heat pulse. For a strike that is on the small end like this that might be just possible, but it may also be too deep still (keep in mind that Sleep was talking of extremophiles that could survive at about 100 C temperature and humans start to wilt even in a hot mine) and active cooling would be a nightmare with Hell above and Hell below. It would definitely require a specially-built shelter far in advance and, moreover, once the disaster was over, returning to the surface would not be of any point since there wouldn't be any ecosystem at all.
TL;DR: "Everybody Dies(TM)" meaning everybody - not just all humans, but all multicellular life and quite likely a sizeable fraction of unicellular life as well. And likely most if not all traces of human civilization as well - the heat is enough to melt down most anything on the surface and certainly incinerate every storage device or method more complicated than a literal stone tablet. (Oddly, buried tablets yet to be dug may have the best odds, even then, depends on how deep the melt goes.) Perhaps the only relic to indicate civilization to any passing aliens might be the magic machine itself - can't remember if SCPs are supposed to be indestructible like the objects in The Lost Room (sad to see they never picked that one up again).
ADD 2: Being in a shelter would be no use in light of the revised mass figure - the cataclysmic seismic kneading would "knead" it into nonexistence in the time it takes for a seismic wave to propagate around the globe (roughly on the order of a kilosecond).
ADD 3: And literally really nothing left, not any trace of humankind - the heat will melt down, down, down, deep, turning the surface into a magma ocean. At least, not on Earth. The only signs will, perhaps, ironically, be our space probes and due to the gamma pulse from the neutronic beta decay process and perhaps initial thermal flash directed upward (we now have to take account of that other half of the energy), the further out the better, and at the very least their electronics stand a strong chance of having been fried to the point of uselessness.
The magnetic field of the teaspoon of the neutron matter would be strong enough to destroy the vending machine before it could do any other weight based damage.
