Nuclei mind map

Nuclei: what the chapter covers

The main idea of each topic with its first key points. Open a branch above for everything, or read the full notes.

1. 1Chapter Overview

   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 physics is mainly about composition, size, stability, force and energy transformations of nuclei.
   • The binding energy curve explains why both fission and fusion release energy.
   • Radioactive decay is statistical; we cannot predict which nucleus decays next, only the average rate.
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2. 2Nuclear Composition

   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 chemical identity of an atom is fixed by Z, not by A.
   • Different isotopes of the same element have similar chemical properties but different nuclear masses.
   • Nuclear radius is extremely small; 1 fm = 10^-15 m.
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3. 3Mass Defect & Binding Energy

   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.

   • Mass defect is not an error; it is the mass equivalent of nuclear binding energy.
   • Packing fraction indicates whether isotopic mass is higher or lower relative to mass number.
   • Binding energy per nucleon is a better stability indicator than total binding energy.
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4. 4Nuclear Forces

   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.

   • Nuclear force is not gravitational; gravity is negligible inside the nucleus.
   • It is not simply electrostatic because it acts between neutrons also.
   • Short-range nature explains why electrons are not held inside the nucleus by nuclear force.
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5. 5Radioactivity

   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.

   • Radioactive decay is probabilistic; λ represents probability of decay per unit time.
   • Half-life is independent of initial number of nuclei.
   • After n half-lives, remaining nuclei = N0/2^n.
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6. 6Nuclear Energy

   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.

   • Fission is used in nuclear reactors and atomic bombs, but reactors use controlled chain reactions.
   • Fusion releases enormous energy and produces stellar energy, but controlled fusion is technically difficult.
   • Criticality depends on neutron multiplication: one neutron from each fission should cause another fission in a steady reactor.
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