Why don't electrons get stuck in the nucleus?

Why doesn't the strong nuclear force attract electrons, when they are under within 10^-15 m of the nucleus?
bkborivli@hotmail.com

This is an interesting question, because if the strong nuclear force could confine the electron within the nucleus, atoms would collapse. Many electrons in the atom do venture very close to the nucleus (especially those in s orbitals). The uncertainty principle comes into play twice here: it determines the range of the strong nuclear force, and it determines the size of the smallest possible space an electron can be restricted to.

How the strong force works. The protons and neutrons in the nucleus are called nucleons. The nucleons are constantly emitting and absorbing little 'messenger' particles called mesons. When one nucleon emits a meson that another nucleon absorbs, a very strong attractive force between the two nucleons results. This is called (strangely enough) the strong nuclear force.

Why is the range of the strong force so small? Production and destruction of the messenger mesons violates the law of conservation of mass & energy! However, if the messenger particle has a very short lifetime, and so exists only within a very small space, the particle can exist within the limitations set by the uncertainty principle. Particles like this are called virtual particles.

If you believe the uncertainty principle, and you believe that nothing can move faster than the speed of light, you can estimate the range of the strong nuclear force as follows. The uncertainty principle says that you can't exactly determine the position and momentum of a very small particle simultaneously. If x is the uncertainty in the particle's position, and (mv) is the uncertainty in the particle's momentum, the uncertainty principle says that

x(mv) = h/2

where m is the particle's mass, v is its velocity, and h is Planck's constant (6.626 × 10^-34 Js). The virtual particle must exist within x = h/2(mc) of the nucleon that generated it. Now, given that the mass of messenger mesons is about 2.5 × 10^-28 kg, and the uncertainty in the velocity can't be any larger than the speed of light (2.9979 × 10⁸ m/s), the virtual particle can't move any more than x = h/(2(mc)) = 1.4 × 10^-15 m from the nucleon that generated it without violating the uncertainty principle or the universal speed limit. That's the range of the strong nuclear force!

Why isn't the electron confined to the nucleus? We can repeat the above calculation for the electron to show that the uncertainty principle forbids it from being restricted to a space as small as an atomic nucleus. The mass of an electron is 9.1 × 10^-31 kg, and it can't move any faster than the speed of light, so the smallest space an electron can be restricted to without violating the uncertainty principle is 4 × 10^-13 m; about 270 times farther than a messenger meson can reach.

Author: Fred Senese senese@antoine.frostburg.edu

Copyright © 1997-2010 by Fred Senese
Comments & questions to fsenese@frostburg.edu
Last Revised 02/23/18.URL: http://antoine.frostburg.edu/chem/senese/101/quantum/faq/electron-confinement-to-nucleus.shtml