Why are neutron rich isotopes unstable

[hwall95]

Ive been researching for a while now and i still can't understand why neutrons rich isotopes are unstable. As neutrons act like the glue and hold protons together as they increase the Strong Nuclear force that act upon protons and neutrons, i thought the more neutrons the stronger they would become.

And second question, is there anyway to know for sure that an isotope is stable, without like researching the isotope or experimentally. Like even if you apply the neutron ratio and magic numbers and the even/even rules, is there also ways a certain level of uncertainty when being theoretical.

 

[bcrowell]

Ive been researching for a while now and i still can't understand why neutrons rich isotopes are unstable. As neutrons act like the glue and hold protons together as they increase the Strong Nuclear force that act upon protons and neutrons, i thought the more neutrons the stronger they would become.

This is because of the Pauli exclusion principle. You fill the proton energy levels up to a certain level, and you fill the neutron energy levels up to a certain level. Let's say you have ten neutrons and two protons, making helium-12:

==
==========

Now instead take 12 nucleons and make 6 of them protons and 6 neutrons:

======
======

The total energy in the second case is much lower than the total energy in the first one. An easy way to see this is to start with the first diagram and take neutrons off of the tall pile and put them on the short pile; they're going down to lower energy states.

And second question, is there anyway to know for sure that an isotope is stable, without like researching the isotope or experimentally. Like even if you apply the neutron ratio and magic numbers and the even/even rules, is there also ways a certain level of uncertainty when being theoretical.

There are models of nuclear structure that can do a better job of this than you can do using these heuristics. For example, a classic application of the nuclear shell model is to predict beta-decay half-lives. However, nuclear structure is a many-body problem, and in general there are no exact, tractable techniques for solving many-body problems. We can't even predict the long-term behavior of our solar system, for example.

 

[hwall95]

hahaha okay i understand why too many neutrons cause instability now and thanks for for mention of the nuclear shell model, ill see if i can apply that as well. Thanks heaps :)