I'm not sure if this question makes sense (if not maybe you can explain why)
But if the neutron has mass and have a size, then it should have a escape velocity in the "surface" right?
I know the gravity force generated by a neutron is really low, since it is also really small in size, what happens with that force when we are really close? is not almost infinite?
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2 Answers
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I know the gravity force generated by a neutron is really low
To define the force, you need to define a second object, with some mass, that is being acted on. That can't be a second neutron, because then there would be an attraction due to the strong nuclear force that would be much greater than the attraction due to gravity. You would want to talk about a particle such as an electron or some other lepton that doesn't participate in the strong force.
what happens with that force when we are really close? is not almost infinite?
The neutron is similar to an object like the earth, in that its mass is distributed over some volume. Therefore you can't get to zero distance from all its mass. The radius of a neutron is roughly 0.8 fm ($10^{-15}$ m). (It's fuzzy, but the number is well defined to within about 20%, if you take some criterion like where the density falls off to half of the value at the center.) Using this radius, the escape velocity is $\sqrt{2Gm/r}=1.7\times10^{-11}$ m/s. The extreme smallness of this velocity confirms that gravity is too weak to matter at the atomic scale.
In reality, if you take a particle such as an electron and try to put it right at the surface of the nucleus, constraining its position to within less than ~1 fm, then by the Heisenberg uncertainty principle, it will be moving many orders of magnitude faster than escape velocity. To get this zero-point velocity to be as small as the escape velocity, you would need a very massive particle -- much more massive than any subatomic particle we know of.
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$\begingroup$ is really low, I canno understand how a black hole can exist then, I mean for a black hole we need a very dense object right? and what is more dense than a neutron? $\endgroup$– EnriqueCommented Apr 17, 2019 at 17:51
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$\begingroup$ @Enrique: To make a black hole, the relevant figure is not density, which would scale like $m/r^3$, but $m/r$. It actually wouldn't make sense if a neutron was an ultrarelativistic object. See physics.stackexchange.com/questions/12404/… $\endgroup$– user4552Commented Apr 17, 2019 at 18:03
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$\begingroup$ Wouldn't a proper escape velocity take into consideration all 4 fundamental forces? $\endgroup$– corsiKaCommented Apr 18, 2019 at 1:10
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$\begingroup$ @corsiKa: If you use an electron, then it's certainly true that the gravitational force would be much weaker than the force exerted by the neutron's dipole field. You could use a neutrino. I doubt that the weak force is significant here. $\endgroup$– user4552Commented Apr 18, 2019 at 22:00
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I'm sure a full quantum mechanical explanation exists that takes complexities at these size scales into account. But using the classical formula for escape velocity ($v_{esc}=\sqrt{2GM/R}$, derived by determining the total amount of work to move a massive point particle from the surface of a massive object to an infinite distance), an estimate of the escape speed using the neutron mass ($1.67\times 10^{-27}$ kg), and radius ($\sim 1.5$ fm) comes to about $1\times 10^{-11}$ m/s.
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$\begingroup$ 1.5 fm sounds more like the diameter, not the radius. $\endgroup$– user4552Commented Apr 17, 2019 at 15:05
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$\begingroup$ It's not well-defined, just an approximation to get an estimate using classical concepts. (en.wikipedia.org/wiki/Atomic_nucleus) $\endgroup$ Commented Apr 17, 2019 at 15:07
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$\begingroup$ It's much better defined than a factor of 2. You simply made a mistake. $\endgroup$– user4552Commented Apr 17, 2019 at 15:08
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4$\begingroup$ My point is using the classical description for escape velocity puts us so far away from precision of that degree that there's no point worrying about it. Call it a mistake if you want. $\endgroup$ Commented Apr 17, 2019 at 15:09