Nuclear Physics: Crash Course Physics #45

Albert Einstein's study of special relativity revealed the equivalence of mass and energy, expressed as E=mc^2. This formula shows that energy is equal to mass multiplied by the speed of light squared, allowing for conversion between these two forms. Mass-energy equivalence underpins nuclear physics, a field exploring atomic nuclei where elements can transform instantaneously into others. It also explains how immense energy resides within atoms.

The nucleus of an atom contains protons, which are positively charged, and neutrons, which have no charge. These particles collectively called nucleons determine atomic properties: the atomic number represents proton count (defining the element), while mass number combines both protons and neutrons. For example, carbon with 6 protons always has an atomic number of 6 but can vary in mass numbers due to differing neutron counts—such as Carbon-12 or Carbon-14 isotopes. Nuclear notation uses a chemical symbol with its atomic number at bottom left and mass number at top left to represent these differences.

Carbon-12 dominates Earth's carbon, with Carbon-14 being rare due to stability when protons equal neutrons. The unified atomic mass unit (u) quantifies nuclear masses, where one u equals 1.6605 × 10^-27 kg. A stable nucleus's total mass is less than its individual components' combined mass; this difference represents the binding energy needed to disassemble it. For example, helium’s nucleus has a lower total mass compared to separate protons and neutrons by an amount equivalent to its binding energy.

Binding energy, calculated using Einstein's equation E=mc², explains the missing mass within a nucleus. The strong nuclear force is an attractive fundamental force that binds protons and neutrons together despite the repulsive electric forces between positively charged protons. This powerful yet short-range force requires additional neutrons to stabilize larger atoms with high atomic numbers by counteracting electromagnetic repulsion. Atoms become unstable when this balance fails, leading their nuclei to break down into more stable configurations.

Radioactivity is the process where unstable nuclei decay, emitting energetic particles. Henri Becquerel discovered natural radioactivity when uranium in a mineral affected a photographic plate despite being covered by paper. Scientists later classified emitted rays into three groups based on their penetration power, with alpha decay involving the loss of two protons and neutrons from an unstable nucleus to form a new element through transmutation. For instance, radium undergoes alpha decay to become radon while releasing an alpha particle (a helium nucleus). The atomic number decreases by two and mass number by four during this transformation.

Mass-Energy Equivalence and Nuclear Decay In nuclear reactions, the total mass of products is always less than that of the parent nucleus due to mass-energy equivalence. This lost mass transforms into kinetic energy, which powers nuclear reactors. Alpha decay emits alpha particles with low penetration power; beta decay involves a neutron converting into a proton while emitting an electron and neutrino through weak force interactions; gamma decay releases high-powered photons as excited nuclei transition to lower energy states without transmutation.

Fundamentals of Nuclear Physics Nuclear physics explores atomic numbers, mass numbers, binding energies, and forces like strong and weak interactions governing nucleons' behavior. Radioactive decays—alpha (low penetration), beta (neutron-to-proton conversion via quark alteration), and gamma (photon emission)—demonstrate how atoms release immense power despite their small size. Concepts such as half-lives or radiocarbon dating further illustrate practical applications derived from these principles.