The Atomic Nucleus
The nucleus is the dense, positively charged core of an atom, containing protons and neutrons (collectively called nucleons). Despite occupying only about one ten-trillionth of the atom's volume, the nucleus contains over 99.9% of its mass. A typical nuclear diameter is roughly 1-10 femtometers (10^-15 m), compared to atomic diameters of about 100 picometers (10^-10 m).
Each nucleus is characterized by two numbers: Z (atomic number, the count of protons) and A (mass number, the total count of protons plus neutrons). Nuclei with the same Z but different A are called isotopes. For example, carbon-12 (6 protons, 6 neutrons) and carbon-14 (6 protons, 8 neutrons) are both carbon isotopes, but their nuclear properties differ dramatically.
The Nuclear Force
Protons carry positive charges and should repel each other violently at nuclear distances due to the electromagnetic force. What holds the nucleus together is the strong nuclear force, one of the four fundamental forces of nature. This force acts between all nucleons (proton-proton, neutron-neutron, and proton-neutron) and is attractive at distances of about 1-3 femtometers.
The strong force is roughly 100 times stronger than the electromagnetic force at nuclear distances, but it drops off extremely rapidly beyond about 3 femtometers. This short range means that each nucleon interacts mainly with its nearest neighbors, a property called saturation. In very large nuclei, the long-range electromagnetic repulsion between all protons eventually overwhelms the short-range strong force, which is why no stable nuclei exist beyond bismuth-209 (Z = 83).
Binding Energy and the Mass Defect
When nucleons come together to form a nucleus, the resulting mass is always less than the sum of the individual nucleon masses. This difference is called the mass defect and is related to energy through Einstein's famous equation:
E = mc^2
The energy equivalent of the mass defect is the nuclear binding energy -- the energy required to completely disassemble a nucleus into separated protons and neutrons. A more useful quantity is the binding energy per nucleon, which measures how tightly each nucleon is held in the nucleus.
The binding energy per nucleon curve peaks at iron-56 and nickel-62, near 8.8 MeV per nucleon. Light nuclei (like hydrogen and helium) have lower binding energy per nucleon, meaning energy is released when they fuse together. Heavy nuclei (like uranium) also have lower binding energy per nucleon, meaning energy is released when they split apart. This single curve explains both nuclear fusion and fission as energy sources.
The Valley of Stability
Plotting all known nuclides on a chart of neutron number (N) versus proton number (Z) reveals the valley of stability, a narrow band where stable nuclei reside. Several patterns emerge:
- Light stable nuclei have roughly equal numbers of protons and neutrons (N approximately equals Z). Examples include carbon-12 (6p, 6n) and oxygen-16 (8p, 8n).
- Heavier stable nuclei require progressively more neutrons than protons to remain stable. Lead-208, the heaviest stable nuclide, has 82 protons but 126 neutrons.
- Magic numbers (2, 8, 20, 28, 50, 82, 126) correspond to completely filled nuclear energy shells. Nuclei with magic numbers of protons, neutrons, or both are exceptionally stable. Helium-4 (doubly magic: Z = 2, N = 2) and lead-208 (doubly magic: Z = 82, N = 126) are prime examples.
- Nuclei with even numbers of protons and neutrons tend to be more stable than those with odd numbers, reflecting the tendency of nucleons to form spin-paired couples.
Nuclear Models
Two complementary models help explain nuclear behavior:
- The liquid drop model treats the nucleus as a droplet of incompressible nuclear fluid. It successfully predicts overall binding energies and explains fission through the competition between surface tension and electrostatic repulsion.
- The nuclear shell model places nucleons in discrete energy levels within a potential well, analogous to electron shells in atoms. It explains magic numbers, nuclear spin, and magnetic moments.
Together, these models provide a comprehensive picture of why some nuclei are stable and others are not, forming the foundation for understanding radioactive decay and nuclear reactions.