Stability of Nuclei

 This simulation is designed for the study of nuclear binding energy and the notion of mass defect. The concept of dependence of the number of neutrons on number of protons in a stable nucleus, as well as dependence of binding energy per nucleon on the element?s mass number are represented graphically. Pick the number of neutrons and protons to build a stable nucleus, and determine the binding energy per nucleon. Atomic nuclei consist of protons and neutrons. The number of protons Z is equal to the element?s number in the periodic table of the elements. The number N designates the total number of neutrons in the atomic nucleus. The total number of protons and neutrons A = Z + N is called the atomic mass number. The nuclei with the same number of protons but a different number of neutrons are known as isotopes of the same element. The general format for an element X with the mass number A and the number of protons Z is AZX, or ZXA. The forces that hold protons and neutrons together are called the nuclear forces. A very important concept in nuclear physics is the concept of binding energy. Binding energy equals to the energy that is required for total fission of the nucleus into separate particles. The binding energy is determined on the basis of a relationship between mass and energy, as postulated by Einstein: E = mc2. Exact measurements of nuclear masses show that the total mass of a nucleus M is always less than the total mass of its constituent parts. The quantity ΔM = Zmp + Nmn - M is called the mass defect. The binding energy equals ΔEB = ΔMc2 where c is the speed of light. The ratio of the binding energy ΔEB of a nucleus to the number of nucleons A is called the binding energy per nucleon: EB = ΔEB/A (MeV/nucleon) . Binding energy per nucleon varies for different nuclei. The dependency of EB as a function of the mass number A is investigated experimentally for all stable nuclides. Except for the lightest nuclides, binding energies per nucleon are about 8 (MeV/nucleon) . This is almost a million times larger than the ionization energy of the hydrogen atom. The nuclei of stable isotopes form only with a definite relationship between the numbers of protons and neutrons. The dots representing stable isotopes on the plane (N, Z) are grouped within the limits of a thin band. For light nuclei, the number of neutrons is approximately equal to the number of protons, but as the mass increases, increase in N outstrips the increase in Z.