Nuclei notes

The chapter Nuclei explains the structure, size, mass and stability of atomic nuclei. A nucleus contains protons and neutrons, collectively called nucleons, and is characterized by atomic number Z and mass number A. The chapter connects nuclear size with A through R = R0A^(1/3), showing nearly constant nuclear density. It then explains why nuclear mass is less than the sum of separate nucleon masses through mass defect and binding energy. Nuclear force is introduced as a strong, short-range, charge-independent and saturating force. Radioactivity describes spontaneous alpha, beta and gamma emissions governed by exponential decay law. Finally, nuclear fission and fusion explain large energy release due to changes in binding energy per nucleon.

Nuclear composition describes what is inside the nucleus and how nuclei are identified. The nucleus contains protons and neutrons, collectively called nucleons. The atomic number Z is the number of protons and determines the element. The mass number A is the total number of protons and neutrons, so neutron number N = A - Z. Nuclides are written as AZX, where X is the chemical symbol. Isotopes have the same Z but different A, isobars have the same A but different Z, and isotones have the same N. Nuclear radius follows R = R0A^(1/3), which means nuclear volume is proportional to A. This leads to almost constant nuclear density for all nuclei.

The mass of a stable nucleus is always less than the sum of the masses of its separate protons and neutrons. This missing mass is called mass defect and is converted into binding energy according to Einstein's mass-energy relation. Binding energy is the energy required to completely separate a nucleus into its nucleons, or equivalently the energy released when the nucleus is formed from free nucleons. Binding energy per nucleon is more useful for comparing nuclear stability. The binding energy curve rises sharply for light nuclei, reaches a maximum near iron and nickel, then slowly decreases for heavy nuclei. Therefore, fusion of light nuclei and fission of heavy nuclei can release energy by moving toward higher binding energy per nucleon.

Nuclear force is the attractive force that holds protons and neutrons together inside the nucleus. This is necessary because protons repel one another electrostatically, yet nuclei remain stable. Nuclear force is much stronger than electrostatic and gravitational forces at nuclear distances, but it acts only over a very short range of about 1 to 2 femtometres. It is nearly charge independent, meaning proton-proton, proton-neutron and neutron-neutron nuclear interactions are approximately similar after ignoring electrostatic repulsion. It also has saturation property: each nucleon interacts strongly only with its nearest neighbours, not with all nucleons in the nucleus. This explains why binding energy per nucleon remains roughly constant for medium and heavy nuclei.

Radioactivity is the spontaneous disintegration of unstable nuclei with emission of alpha particles, beta particles or gamma rays. It is a nuclear phenomenon and is almost unaffected by temperature, pressure, chemical state or external physical conditions. In alpha decay, the nucleus emits a helium nucleus, so A decreases by 4 and Z decreases by 2. In beta-minus decay, a neutron converts into a proton, so Z increases by 1 while A remains unchanged. In beta-plus decay, a proton converts into a neutron, so Z decreases by 1. Gamma decay emits high-energy photons from an excited nucleus without changing A or Z. The number of undecayed nuclei follows exponential decay, leading to half-life, mean life and activity concepts.

Nuclear energy is released when nuclear reactions produce products with higher binding energy per nucleon than the reactants. In nuclear fission, a heavy nucleus such as uranium-235 absorbs a neutron and splits into two medium-mass nuclei along with more neutrons and a large amount of energy. These neutrons can trigger further fissions, producing a chain reaction. A nuclear reactor controls this chain reaction using moderator, control rods, coolant and shielding. In nuclear fusion, two light nuclei combine to form a heavier nucleus and release energy; this powers the Sun and stars. Fusion requires extremely high temperature because positively charged nuclei must overcome electrostatic repulsion before nuclear force can bind them.