(thought you have to understand, if it were, the opposing charges of the particles would hold it together, NOT make it fall apart)
the nucleus is made up of positive particles (protons) and neutral particles (neutrons). electrons are always NEGATIVELY charged and are not in the nucleus.
while it is true that atoms are made of positive and negative charges wich attract, the protons in the nucleus should repel based on this theory. the reason why the nucleus stays together is because there is a nuclear force that supercedes the magnetic and gravitational forces. neutrons that have a neutral charge also help the nucleus stay together because they buffer between protons.