# Electrostatic force has longer range than strong nuclear force?

In my revision guide it says that the electrostatic repulsion between protons in a nucleus has a longer (indefinite, actually) range than the strong nuclear force keeping the nucleons together. So I thought: If this is true, what happens at very large separations, e.g. in stable atoms with a large nucleus. The strong nuclear force wouldn't be holding the nucleons together, so what is keeping them from flying apart?

Thanks

• The atoms with the largest nuclei are not stable and fly apart in exactly the fashion you describe. May 8 '15 at 11:06
• Yes, but there are heavy nuclei that are not too large to be unstable. It's complicated business, but for a rough picture we can note that each nucleon is up against its immediate neighbors. The aggregate of local strong forces can dominate the aggregate Coulomb repulsion, leading to overall stability. May 8 '15 at 13:07
• possible duplicate of Why is the strong nuclear force > electrostatic repulsion? May 9 '15 at 5:34

The electrostatic force has an infinite range and it falls down with distance in an inverse square power law

$$F_e \propto \frac{1}{r^2}$$

while the strong nuclear force behaves quite differently as it exhibits a property called confinement.

Confinement is still to be understood (it is related to one of the millennium prizes), but heuristically you can think of it as a force (for example acting on a pair of quark and anti-quark) that grows linearly with distance

$$F_s \propto r$$

just like a stretched spring. Although quite stronger than the electrostatic force, it happens that $r$ cannot stretch ad infinitum as the spring breaks into two pieces

and as such there is somehow a maximum distance after which the strong force does not attract any more.

As such nuclei, as you pointed out, will not be stable after some size as the electrostatic force will be the predominant force, which is repelling protons from each other.

• This answer appears to explain why nucleons decay. My reading of the OP is that the question is about stability of the nucleus, for which the nucleons remain more or less intact. Although this answer has been accepted, and it does explain something, I'm not sure it really answers the question. May 8 '15 at 13:02
• @garyp The two are related since one potential way to achieve stability of a nucleus with too many protons is for a proton to decay into a neutron, though now we need to bring up the weak force too. Though I agree with you, I thought the question was about large nuclei, which is complicated since it a residual force on color neutral nucleons. May 8 '15 at 13:15
• No worries OP glad it helped. @garyp , my understanding was that the OP was asking about the relations and balances between the two forces at play in the nucleus and how it relates to the size and stability. The OP seemed happy with what I provided, I hope I didn't mislead him with a misleading answer. May 8 '15 at 14:33