The composition of a nuclide (atomic nucleus) is defined by the number of protons Z and the number of neutrons N, which sum to mass number A. Proton number Z, also named the atomic number, determines the position of an element in the periodic table. The approximately 3300 known nuclides are commonly represented in a chart with Z and N for its axes and the half-life for radioactive decay indicated for each unstable nuclide (see figure). , 251 nuclides are observed to be stable (having never been observed to decay); generally, as the number of protons increases, stable nuclei have a higher neutron–proton ratio (more neutrons per proton). The last element in the periodic table that has a stable isotope is lead (Z = 82), with stability (i.e., half-lives of the longest-lived isotopes) generally decreasing in heavier elements, especially beyond curium (Z = 96). The half-lives of nuclei also decrease when there is a lopsided neutron–proton ratio, such that the resulting nuclei have too few or too many neutrons to be stable.
The stability of a nucleus is determined by its binding energy, higher binding energy conferring greater stability. The binding energy per nucleon increases with atomic number to a broad plateau around A = 60, then declines. If a nucleus can be split into two parts that have a lower total energy (a consequence of the mass defect resulting from greater binding energy), it is unstable. The nucleus can hold together for a finite time because there is a potential barrier opposing the split, but this barrier can be crossed by quantum tunneling. The lower the barrier and the masses of the fragments, the greater the probability per unit time of a split.
Protons in a nucleus are bound together by the strong force, which counterbalances the Coulomb repulsion between positively charged protons. In heavier nuclei, larger numbers of uncharged neutrons are needed to reduce repulsion and confer additional stability. Even so, as physicists started to synthesize elements that are not found in nature, they found the stability decreased as the nuclei became heavier. Thus, they speculated that the periodic table might come to an end. The discoverers of plutonium (element 94) considered naming it "ultimium", thinking it was the last. Following the discoveries of heavier elements, of which some decayed in microseconds, it then seemed that instability with respect to spontaneous fission would limit the existence of heavier elements. In 1939, an upper limit of potential element synthesis was estimated around element 104, and following the first discoveries of transactinide elements in the early 1960s, this upper limit prediction was extended to element 108.