So if you collapsed Mount Everest (estimated mass 6.4 trillion metric tons) into neutronium, it would be about 64 cc of neutronium, roughly a quarter-cup. If you set that little blob of neutronium on the ground (like you could keep it from getting there anyway) it would sink right through the rock to the Earth's core--but once there the momentum it had acquired on the way there would prevent it from stopping, and it would proceed to orbit the Earth's center of mass--for a while--growing bigger as it did. Eventually the drag of passing through the mantle and core of the Earth would slow it to a stop at the center of the planet, where it would continue to absorb the Earth's mass, eventually turning the entire planet to neutronium.
A blob of neutronium massing 6 x 1021 metric tons would be 600,000 cubic meters in volume, making it a sphere about 126 meters in diameter.
This way lies ruin. Literally. But on the plus side, I don't think the Moon would ever notice the difference.
* * *
This is what happens: I learn a new fact about something interesting, and I run with it. I've wondered what the actual density of neutronium was for quite a while, but never actually got around to taking the guestion to Googe or what-have-you.
Then--having run literal back-of-the-envelope calculations--I emit a happy little chuckle that I again worked out something technical from basic principles.
I also learned that a bare neutron--say, one that's been emitted from a fissioning nucleus--has a half-life of about ten minutes before it undergoes beta decay and turns into a proton, electron, and some extra energy. Ten minutes is enough time for light to travel 1.25 AU, about 116,250,000 miles. So if you come across some anomaly that spits a torrent of neutrons, and all you have to protect you from it is a magnetic field, you want to stay at least 3-5 AU away from the thing. (Your magnetic field will protect you from protons and electrons, but not neutrons.)
Oh, but guess what?
A teaspoon of degenerate neutronium gas would have a mass of two billion tonnes, and if moved to standard temperature and pressure, would emit 57 billion joules of β− decay energy in the first half-life (average of 95 MW of power).So instead of falling through the Earth and converting it to neutronium, you'd just get this big continuous explosion for an hour or so, and then it'd be over. 95 MW over ten minutes--while it's a lot of power, some 159 KW per second--it's not a world-ending amount.
Let's put that into perspective. 57 gigajoules from the teaspoon of neutronium? TNT contains about a million joules of energy per kilogram. Compare that to 100 million (0.1 gigajoule) for a gallon of gasoline. 159 kilowatt-seconds is 159,000 joules, roughly the power output of a good six-cylinder engine, or else it's the energy released by 0.159 kilograms of TNT detonating. (An eighth stick of dynamite, more or less.)
In other words, it would suck to be within, oh, five miles or so of where Mount Everest used to be--but only because of the beta radiation. Otherwise things ought to be okay. And the first half-life--the first ten minutes--would be the worst, because necessarily the intensity of the emitted radiation would drop by half thereafter. After six half-lives--about sixty minutes--the intensity would be 1/64th as it was initially. Two hours after Mount Everest turned quite unexpectedly into neutronium, it would be completely safe to venture into the crater. (It would be "mostly safe" about ninety minutes after.)
...I would have thought it would be worse than that--a huge explosion--but the numbers don't lie.
* * *
This sort of stuff looks like wizardry, but it really isn't. It's knowing a few salient facts and being able to put them together, and understanding how they relate. Everyone does much the same thing within his specialty, whether it's laying bricks or operating machine tools or what-have-you. I can learn how to do those things, but the people who routinely do those things could also learn to do this. It's not that complicated.
* * *
Anyway, that's enough science-fictional musing for one day.