If I had a container of neutrons 1 litre big, how much would it weigh?
Assume that I actually have something strong enough to withstand the mass and pressures involved so the sides of the box don’t collapse and ground is also able to support the box. Also, the box doesn’t have a lid so there is nothing to stop the matter from expanding upwards if it needs to. If you need to tweak my experiment to get it to work do so but let me know what you would have to do and why e.g. If the neutrons will fly apart due to the temperature then let’s assume we have cooled the box down to as close to absolute zero as we can.
If I do my (probably incorrect) calculations I get the following
Neutron Mass (NM) = 1.7×10[sup]−27[/sup] kg
Neutron Radius (NR) = 1x10[sup]-13[/sup]cm
Neutron Volume (NV) = 4/3.π.NR[sup]3[/sup]=4.2x10[sup]-39[/sup]cm[sup]3[/sup]
Neutron Density (ND) = NM / NV = 1.7x10[sup]-27[/sup]kg/4.2x10[sup]-39[/sup]cm[sup]3[/sup] = 0.4 x 10[sup]12[/sup]kg/cm[sup]3[/sup] = 4 x 10[sup]11[/sup]kg/cm[sup]3[/sup]
(I just came across the density of the atomic nucleus on Wikipedia and it as about 3 x[sup]17[/sup]kg/m[sup]3[/sup] which is pretty
close to my neutron density calculation - I guess those high school lessons actually stuck in my head)
Assuming that neutrons are spheres then we can pack them with about 70% efficiency and a litre is 1000cm[sup]3[/sup] this means that 1 litre of neutrons will weigh about ND0.71000 kg or 2.8x10[sup]14[/sup]kg or 280 000 000 000 000kg.
An interesting fact then is Mount Everest weighs about 3x10[sup]15[/sup]kg according to one site on the internet so Mount Everest weighs about the same as 10 of my litre boxes of neutrons.
Are my calculations correct?
What would stop me from having a theoretical container of neutrons? I see that neutrons have a half life of a little under 15 minutes so I suppose that if the neutrons start decaying they might cause other nuclear reactions inside my box and blow the whole thing apart but let’s assume that I only need the box for a fraction of a second so we can discount the half-life of the neutrons. However, if I did leave my box alone for a couple of hours what would probably happen due to the neutrons decaying?
I know a box of neutron star material cannot be brought to earth because it will violently expand due to there being no intense gravity field to keep it compressed but will my box be stable even though it is extremely heavy. There will be no repulsion between the neutrons because they are electrically neutral so what would stop then from touching each other? I know that the Pauli Exclusion Principle can stop particles from getting too close to each other but does this apply to the neutrons in my scenario? Neutrons in neutron star are packed denser so I assume not.
Thanks in advance for your input and I await your answers with interest.
A typical neutron star has a mass between 1.35 and about 2.0 solar masses, with a corresponding radius of about 12 km if the Akmal-Pandharipande-Ravenhall equation of state (APR EOS) is used. In contrast, the Sun’s radius is about 60,000 times that. Neutron stars have overall densities predicted by the APR EOS of 3.7×1017 to 5.9×1017 kg/m3 (2.6×1014 to 4.1×1014 times the density of the Sun), which compares with the approximate density of an atomic nucleus of 3×1017 kg/m3. The neutron star’s density varies from below 1×109 kg/m3 in the crust, increasing with depth to above 6×1017 or 8×1017 kg/m3 deeper inside (denser than an atomic nucleus). This density is approximately equivalent to the mass of the entire human population compressed to the size of a sugar cube.
The problem with a neutron star is that it’s intense gravity is what keeps the neutrons together, I want to know what happens if I fill a box with neutrons in an earth type environment.
I dunno, but the op might find the wiki page on Neutronium interesting. In any event, you’d better measure fast - within 15 minutes, free neutrons decay.
Probably not; you calculated the weight of the contents but forgot to account for the weight of the container itself, which would have to be pretty massive in order to support that volume of neutrons.
Your setup makes no sense even assuming ultra strong materials. I think you are confusing or conflating a few issues. Other than magic the only thing that will allow for super dense neutron packing is an extremely powerful gravity field which is more or less exactly the same hypothetical as bringing dwarf star material to earth and having it go “kaboom”. Super dense neutron packing without hyper gravity is impossible, period.
Image I have a small container that is 10 neutrons big and I put 2 neutrons in it, how close will those those 2 neutrons be? What happens if I put 10 neutrons in it? What happens if I scale this container up to a litre size and now fill it will neutrons and what will it weigh? My question is not about super dense packing but rather about how the neutrons will pack in a normal earth enivronment.
Basically these are questions I am curious about - what happens if you pour neutrons into a container, if I fill up a litre container with neutrons how heavy will it be and what, if any, “strange” side-effects can I expect from doing this?
I suspect that the problem is that the decay of neutrons is turning those tightly packed neutrons into protons and electrons (plus neutrinos) very quickly. Pretty soon after they will bang round enough to organise themselves into hydrogen atoms (as well as heating everything up) and you will have to deal with what amounts to an explosion of hydrogen blasting apart your container load only picoseconds after it is created. Calculate the size of a hydrogen atom, and calculate the conversion rate. 280 000 000 000 000 kg of neutrons will turn into 140 000 000 000 000 kg of hydrogen after 15 minutes. Very roughly, after 3 picoseconds you already have a kilogram of hydrogen. No container technology is going to survive the next few picoseconds. After that it is all downhill, and lots of hydrogen.
I note that in the first few picoseconds the rate of expansion probably forces the container’s boundary to expand faster than the speed of light - so there will be some effective pressure seen by the container’s contents for a short while. But soon enough you will simply have to contend with a LOT of hydrogen, and a lot of heating.
Overall, any container holding free neutrons, of any density is probably going to be limited by the dual problems of heating due to decay, and production of hydrogen. You might therefore assume that the density of neutrons you can cope with is of a similar order to ordinary matter.
The point is that, sans hyper-gravity, or generating them as an energetic beam you can’t isolate and “pack and stack” neutrons by themselves as they are coupled with other particles.
Remember, everyone, the OP is assuming the container is under Earthly conditions (he left the top of his box open), not that we somehow have a chunk of neutron star in the box. Which actually makes it a very simple problem. Under Earthly conditions of temperature and pressure, the neutrons would form a gas, for which the ideal gas law would provide an excellent approximation. Under such conditions, the size of the particles themselves have basically no effect on how much space they take up: That’s all governed by their motions and their bounces off of each other and their container. A given number of gas particles, at a given temperature and pressure, will always take up exactly the same amount of volume, no matter what the particles are.
For any gas at standard temperature and pressure, 1 mole of particles will take up a volume of 22.4 liters, and a mole of neutrons is 1 gram. So your 1-liter bucket of neutrinos will contain about 0.04 grams of neutrinos.
The only real difficulty here is that neutrons, being uncharged, penetrate ordinary matter very easily, so you’d have a hard time making a bucket to hold them. That’s a much easier engineering problem than making a container to hold neutron star material, though.
Oh, and astro, the thread you linked there is over a decade old, and I’d like to say for the record that I no longer entirely stand by the post I gave in it.
Chronus, that’s an very and not one I expected although it makes sense. I found an Ideal Gas Law calculator on the internet that calculates at one atmosphere and 1K, 1 litre will contain about 12 moles so the mass hasn’t increased dramatically with a lower temperature. At 0.000001K, 1 litre will contain about 12100000 Moles or about 12100kg and now the weight starts to climb. Would this be correct? I would guess not because the Ideal Gas Law is for a hypothetical ideal gas and not for Neutrons or any other “normal” gas in an extreme environment.
Anyhow, I guess the bottom line is that the neutrons will behave like a gas.