In a nucleus there is a gravitational force between the nucleons and also electrostatic repulsion between the protons, and since electrostatic repulson >> gravitational attraction, it follows that there must be an additional attractive force acting on the nucleons or else there is nothing stopping them from flying apart.

So if we let the gravitational and electrostatic forces be $g$ and $e$, respectively, and denote the additional attractive force by $x$, then we would need $g+x=e$ (because the attractive and repulsive forces must balance).

This gives $x=e-g<e$, implying that the additional attractive force must be less than electrostatic repulsion. Since the strong nuclear force must be part of $x$, we then have strong nuclear force $\le x<e$.

But in my revision guide, it says that the strong nuclear force is more than electrostatic repulsion, which seems counter-intuitive according to the above.

Please explain!

  • 2
    $\begingroup$ "then we would need $g+x=e$ (because the attractive and repulsive forces must balance)" You are thinking of nucleons like little billiard balls and that model isn't really appropriate in this intrinsically quantum realm. That equality does not hold. $\endgroup$ Commented May 7, 2015 at 18:57
  • $\begingroup$ @dmckee: Thanks! But is there still an intuitive quantum explanation for why strong force > electrostatic repulsion? $\endgroup$
    – user45220
    Commented May 7, 2015 at 19:06

1 Answer 1


Consider the Earth-Moon system. They are subject to an attractive force (gravitation) and to no repulsive forces (neglecting solar tides, anyway), yet they stay at a nearly constant distance from one another because of their dynamics.

A a static analysis of this system would prompt us to postulate some repulsive force holding the bodies apart (and you can find it by using a non-inertial frame of reference: it is the centrifugal pseudoforce). The lesson is that static analysis will break when applied to dynamic systems.

You are trying to analyze the nucleus in terms of statics when it is a dynamic system (and moreover a dynamic quantum system). As nuclear particles are confined to a limited region in space they necessarily acquire a larger range of momenta as a consequence of the commuter between positions and momentum (we can wave our hands and say "Heisenberg Uncertainty Principle" if you want a shorter label for this effect).

  • $\begingroup$ @dmckee in the Feynman lectures, Feynman said that the nuclear force can be approximated as $F=(1/r^2)exp(-r)$. It seems to me that although it falls off really fast, it has infinite range. So how come it has short range? $\endgroup$
    – Omar Nagib
    Commented Jul 13, 2015 at 17:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.