A Limit to the Size of a Nucleus

The strong force that holds the nucleus together is a very short range force, significant on a scale of a few times
$10^{-15}$
n. For distances only slightly larger than this it falls off rapidly. Even though it operates on all nucleons - protons and neutrons - and is always attractive, its short range limits the size of a nucleus. This limit arises because then electrostatic force inside the nucleus is always repulsive, since all the charges inside the nucleus are positively charged - protons - or neutral - neutrons, and obeys an inverse square law, so that the repulsive force increases rapidly with decreasing distance. AIf you make the nucleus bigger by adding more neutrons and protons, the repulsive electrostatic force increases more rapidly inside the nucleus than the attractive strong force and overwhelms it.
Even before this limit is reached, the increasing relative strength of the electrostatic force has effects, in the decreasing stability of the nucleus as the size of the nucleus increases. Nuclei heavier than iron show a tendency to decay by fission, becoming smaller and more stable. Studies indicate that the largest possible nucleus contains about 7,000 nucleons, but well before this stage is reached, nuclei become very unstable, with lifetimes typically a fraction of a second. In fact only about 10% of the 3,000 known isotopes are stable, with the unstable isotopes concentrated among the largest nuclei.