Do protons repel each other?

Particles that have the same charge, or like charges, will repel each other. This applies to the positively charged protons and the center of the atom. Because they share like charges protons do ten to repel each other. The inverse of this is that the protons, which are heavier, larger, and denser than the electrons, are attracted to the electrons due to the opposite and equal negative charge of the electrons.

The lighter and much smaller electrons do most of the moving in an atom. Because of the higher weight and density of the protons, their tendency to repel each other and the counterbalancing attraction to the electrons rotating around them, the protons really do not move very much and remain stable.

The only instance where protons repelling each other would not be a factor would be for hydrogen atoms, which only contain one proton in the nucleus. The one proton in the nucleus of the hydrogen atom is the only positively charged particle of the hydrogen atom.