Protons exist at the center of atoms, specifically in the atomic nucleus, because they carry a positive electric charge. The nucleus is composed of protons and usually neutrons, which are neutral particles. The positive charge of the protons is balanced by the negatively charged electrons that occupy the space surrounding the nucleus.
On the other hand, electrons are not located at the center of atoms because they have a negative charge and are strongly attracted to the positively charged protons. According to the laws of electromagnetism, opposite charges attract each other, so the negatively charged electrons are drawn towards the positively charged nucleus. However, due to the wave-like nature of electrons and the principles of quantum mechanics, electrons do not occupy specific positions like planets around the Sun but exist in regions of space called orbitals or electron clouds. These orbitals represent the probability distribution of finding an electron at a given location around the nucleus.
In summary, protons exist at the center of atoms because they carry a positive charge, while electrons occupy regions around the nucleus due to their negative charge and the principles of quantum mechanics. The interaction between the positive protons and negative electrons creates the overall stability of the atom.