Why are there usually more neutrons than protons in a heavy element? Has Pauli's exclusions principle got anything to do with it?

Asked by: Ciaran Mc Keown

Answer

The reason is that protons, being charged particles, repel each other. As you get to heavier elements, with each new proton you add, there is a larger repulsive force. The nuclear force is attractive and stronger than the electrostatic force, but it has a finite range. So you need to add extra neutrons, which do not repel each other, to add extra attractive force. You eventually reach a point where the nucleus is just too big, and tends to decay via alpha decay or spontaneous fission.

To view this in quantum mechanical terms, the proton potential well is not as deep as the neutron well due to the electrostatic repulsion. [Due to the Pauli exclusion principle, you only get two particles per level (spin up and spin down)]. If one well is filled higher than the other, you tend to get a beta decay to even them out. As the nuclei get larger, the neutron well gets deeper as compared to the proton well and you get more neutrons than protons.
Answered by: Tom Swanson, Ph.D., Physicist, US Naval Observatory