text: All atomic nuclei are composed of protons and neutrons bound together by the nuclear force. There are 286 primordial nuclides that occur naturally on earth, each corresponding to a unique number of protons, called the atomic number, Z, and a unique number of neutrons, called the neutron number, N. The mass number, A, of a nuclide is the sum of atomic and neutron numbers, A = Z + N. Not all nuclides are stable, however. According to Byrne, stable nuclides are defined as those having a half-life greater than 10 years, and there are many combinations of protons and neutrons that form nuclides that are unstable. A common example of an unstable nuclide is carbon-14 that decays by beta decay into nitrogen-14 with a half-life of about 5,730 years:
  In this form of decay, the original element becomes a new chemical element in a process known as nuclear transmutation and a beta particle and an electron antineutrino are emitted. An essential property of this and all nuclide decays is that the total energy of the decay product is less than that of the original nuclide. The difference between the initial and final nuclide binding energies is carried away by the kinetic energies of the decay products, often the beta particle and its associated neutrino.
  The concept of the valley of stability is a way of organizing all of the nuclides according to binding energy as a function of neutron and proton numbers. Most stable nuclides have roughly equal numbers of protons and neutrons, so the line for which Z = N forms a rough initial line defining stable nuclides. The greater the number of protons, the more neutrons are required to stabilize a nuclide; nuclides with larger values for Z require an even larger number of neutrons, N > Z, to be stable. The valley of stability is formed by the negative of binding energy, the binding energy being the energy required to break apart the nuclide into its proton and neutron components. The stable nuclides have high binding energy, and these nuclides lie along the bottom of the valley of stability. Nuclides with weaker binding energy have combinations of N and Z that lie off of the line of stability and further up the sides of the valley of stability. Unstable nuclides can be formed in nuclear reactors or supernovas, for example. Such nuclides often decay in sequences of reactions called decay chains that take the resulting nuclides sequentially down the slopes of the valley of stability. The sequence of decays take nuclides toward greater binding energies, and the nuclides terminating the chain are stable. The valley of stability provides both a conceptual approach for how to organize the myriad stable and unstable nuclides into a coherent picture and an intuitive way to understand how and why sequences of radioactive decay occur.