Mdthbs

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?

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

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

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.

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 hours. Oh, and the mega crater at wherever the office with the vending machine was located.

I don't have the full answer you're looking for - exactly how much damage will be done - but that is definitely going to explode, very spectacularly. And the vapour that used to be your coffee cup will be radioactive.

You suddenly have more stuff in your cup than should reasonably exist in your whole building. The pressure will, eventually, equalise. There will be a shockwave while that works itself out.

Free neutrons will not exist for more than a few minutes at Earth pressure. They would decay, releasing a lot of energy. Unless they collide with an atom first, which will tend to make the atom unstable (ie radioactive). There are more free neutrons in that cup than there are atoms in your office, so this isn't going to be pleasant.