# How come stable isotopes have more neutrons than protons?

by dingo_d
Tags: isotopes, neutrons, protons, stable
 P: 211 So, watching the chart of isotopes (or nuclides), where I have isotopes put according to how stable they are, I have seen that the stable elements have more neutrons than protons. And I wonder why that is? Is it because neutrons are responsible for binding the nucleus with nuclear force (because protons would just repel each other due to Coulomb force), and contribute to higher binding energy or is it something else? I'm taking nuclear physics class, but we only deal with mathematical side like transitional matrix elements and quadrupole moment etc. Plus the professor is kinda boring. And I'd like some nice explanations to why some things are. So if you can help me understand this a bit better I'd be grateful :)
 P: 617 There are a lot of ways to answer this question but the bottom line is that the nuclear force dies off quicker as a function of distance than does the electric force. With a larger nuclear radius, opposite sides are farther apart and therefore the electric force repelling protons is, per nucleon, stronger than the nuclear force attracting everything. To get a stable nucleus, you have to compensate for this by adding more neutrons so that that total nuclear binding force balances the repellant force. If you look closely, stable elements with small diameters (He, Li, etc.) have roughly equal amounts of neutrons and protons. As you go to bigger and bigger nuclei, you need disproportionally more neutrons to keep the nucleus stable.
 P: 211 So basically it's all because of the force, that is competition between Coulomb repulsion and nuclear force. Thanks for the clarification :)
P: 546

## How come stable isotopes have more neutrons than protons?

Also, note that for lighter elements, isotopes with equal numbers of protons and neutrons are typically stable, as is Helium-3 (and, trivially, Hydrogen-1).
 P: 743 Hmm, this explains why too few neutrons is unstable, but why is too many neutrons unstable?
P: 5,776
 Quote by Khashishi Hmm, this explains why too few neutrons is unstable, but why is too many neutrons unstable?
I am guessing, but it may be related to the fact that free neutrons are unstable.
 Mentor P: 9,631 Protons and neutrons are fermions, therefore they cannot have identical quantum numbers in the nucleus. This means that only two neutrons can occupy the lowest state (with spin up and down), the following two neutrons have to use a state with higher energy and so on. If you have too many neutrons and too few protons, the highest occupied neutron state has a higher energy than the lowest free proton state (plus electron plus neutrino energy), and a neutron can decay into a proton. This is the main reason why the total number of stable nuclei with fixed sum of protons+neutrons is very small - usually just one. The coulomb forces just increase the proton energy levels a bit and therefore reduce the proton to neutron ratio for large nuclei, but they do not make every nucleus with some additional protons unstable.

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