How many neutrons there should be to keep an atom stable

[Myslius]

(1) Is there any equation to determine how many neutrons there should be to keep an atom stable? I don't mean mass - number of protons. I mean the equation that can determine an interval of neutrons based on atomic number only and the forces.
(2)Why can't there be an hydrogen atom with 6 neutrons?
(3) Do neutrons repel each other? Isn't there enough space for neutrons to make for example hydrogen atom with 6 neutrons?
(4) How to calculate the heaviest possible atom? How come there exist a limit for atoms? I know that + repels +, but neutrons keep protons together. What kind of other forces are involved in this process except electromagnetism?
(5) Why for example exist U236 and U238 isotope, but not U237 isotope, what makes this difference?
(6) Can an atom be modeled? For example protons and neutrons are put in sequence to keep an atom even more stable or even to create new stable atoms?
(7) Do every isotope acts the same? Have the same properties? U238 will have the same half-life, or it is just an average?

A lot of questions in my head, I'm looking for some math, formulas, papers, and most of all answers. thank you

 

[Drakkith]

Alright! Lemme put my thinking cap on! (I hope this is all correct, I'm working from memory from several sources.)
I can't provide you with the math and the formulas and stuff, but hopefully this helps.

First, there are 4 fundamental forces. Gravity, Electromagnetism, the Weak Force, and the Strong Force.

You already know that the electromagnetic force causes + to repel + and such, and I'm assuming you know what gravity is. Now, protons and neutrons are composite particles. They are both made up of 3 particles called Quarks. A proton has an Up, Up, Down collection of quarks, while a neutron has an Up, Down, Down collection. These quarks experience something called the Strong Force. This is what holds them together and, similar to how electromagnetism holds atoms together with other atoms, it holds nucleons together in the nucleus.

Now, a Down quark is more massive than an Up quark. That means that a neutron is more massive than a proton. A neutron that is NOT inside a nucleus and is simply free by itself in space is known as a Free Neutron. These nuetrons decay into protons with a half life of about 12-13 minutes by changing one of their Down Quarks into an Up Quark. Why? Because a proton is less massive and is a lower state of energy than a neutron is.

So, why doesn't it do that inside a nucleus? It doesn't because protons repel each other, and changing into a proton would result in a state that was GREATER in energy than it was with the neutron there. Neutrons basically provide extra Strong Force to hold the nucleus together. But, if you have enough strong force to hold it together, adding MORE neutrons is unnecessary! So by adding more you are INCREASING the energy state of the nucleus. This is similar to trying to add more electrons to an atom than there are protons.

Lets look at Hydrogen. Simple hydrogen with 1 proton and 1 electron is stable because a proton is the lowest mass nucleon and an electron perfectly cancels out its electric charge. Hydrogen also comes in an isotope with 1 neutron called Dueterium. This is also stable. Why? Because it basically requires less energy for a neutron and a proton to exist bound together in a nucleus than either of them seperate.

Now let's look at Tritium, another Isotope of Hydrogen with TWO nuetrons. Tritium is NOT stable and has a half life of around 12 years I believe. Since Deuterium already had 1 nuetron to pair with it's proton, trying to add another causes that one to exist in a higher energy level than the other two without something for it to bind to. (It still is attracted to both other nucleons, but I'm trying to avoid getting too detailed.) So eventually the atom decays into Helium by converting that Neutron into a Proton. Some isotopes with too few nuetrons can turn a proton into a neutron to make itself more stable.

So that's "basically" why certain amounts of neutrons are needed while having too many or too little results in radioactive decay. It might not be EXACTLY correct but it's a good way to look at it.

Now, a few other things. First, the concept of "Space" is meaningless. All nucleons are effectively occupying the same "Space" inside a nucleus. Instead of space think of energy levels.

Isotopes generally (but not always) act very similar to their similar counterparts for most circumstances. The only one I know that has a noticeable difference is Deuterium. If you replace normal water with "Heavy Water" inside a living organism, which is water whose Hydrogen atoms are Deuterium instead, it compounds certain actions like cell division. This is because Deuterium is twice as massive as normal hydrogen. However this is a special case because out of all stable isotopes Deuterium has the most difference in mass from it's normal counterpart. Most isotopes weigh a fraction heavier or lighter, not twice or half.