Atomic, Nuclear & Particle Physics: From Beginner to Expert

Explore atomism through classical models of the atom. Preview quantum models and identify mass, charge, and spin as key quantities, shaping gravity and electromagnetism.

Trace the evolution of atomic models from a uniform sphere to quantum and nuclear theories. Learn how scattering, charge, mass, spin, and quarks shape the standard model and fundamental forces.

Explore the history of atomism and elements from atomos to Plato’s elemental theory, contrasting discrete atoms with continuous matter and the finite atoms idea that leads to Dalton’s model.

Explore Dalton's atom model, built on conservation of mass and the law of definite proportions. Relate multiple proportions to atom and molecule ideas, and note Dalton's notable mistakes.

Explore how mass and force intertwine through Newton's laws, illustrating inertia, acceleration, and momentum, with gravity and everyday examples to connect to particle physics foundations.

Explore gravity as a fundamental interaction, deriving its 1/r^2 form from Newton's third law and comparing near-earth gravity to the general law via the moon's orbit.

Dalton linked mass to element identity, enabling measurement of mass. Ionized atoms deflect in a magnetic field via the Lorentz force, revealing mass; this is the principle of mass spectroscopy.

Engage with challenging exercises in atomic and nuclear physics, spend time solving tasks, and review the provided solutions to connect outcomes to atomic models.

Practice calculating the charge and mass of ions by analyzing a 90-degree deflection in a 10 mT magnetic field at 1000 m/s in a mass spectroscopy exercise.

Calibrate a mass spectrometry device using known ion masses to compute radii in a magnetic field, then deduce unknown masses from displacement.

Explore how Dalton's mass concept led to the periodic table, with Mendeleev grouping similar elements into eight groups and leaving gaps for unknowns, later tied to quantum mechanics.

Introduce charge as a property alongside gravity and mass. Show how rubbing amber with fur transfers charge, creating negative and positive charges and electrostatic interaction, precursor to the electromagnetic interaction.

Explore how charges repel or attract, underpinning the electromagnetic interaction, construct the electric field, and express forces via qE and the Lorentz force F = q(E + v×B).

Thomson's 1897 cathode ray experiment reveals electrons as subatomic particles with a tiny mass, showing the mass-to-charge ratio is independent of cathode material and enabling later measurements.

Apply the Millikan experiment to measure the electron charge using levitating oil drops in an electric field. Observe peaks at multiples of the elementary charge, ~1.6e-19 C.

Measure the electron's negative charge with Millikan's experiment, and determine its mass with Thomson's deflection, showing the electron is a tiny, light subatomic particle far smaller than an atom.

Practice calculating the electron mass from its charge by deflecting accelerated electrons in a known electric field, using a Thomson–Millikan style setup with 0.1 V/m field and a 60° angle.

Determine the electron mass by linking electrostatic force qE to vertical acceleration inside a 1 cm electric field, using vx and a 60-degree deflection.

Thomson's plum pudding model placed electrons in a positively charged background, creating a neutral atom and a subatomic structure. Millikan's experiment measured the electron's charge and challenged Thomson's model.

Explore scattering experiments that contradicted Thomson's model, revealing the nucleus through alpha-particle gold foil experiments and the phenomenon of back scattering.

Identify Rutherford's positively charged nucleus with electrons, updating Thomson's view. Link Dalton, Thomson, and the nucleus while noting peaked emission and absorption spectra that motivate quantum ideas.

Explore how to estimate the nuclear radius using alpha-particle scattering and Coulomb force. Apply energy conservation to find the closest approach and set an upper limit on nuclear sizes.

Apply energy conservation to relate kinetic energy to electrostatic (Coulomb) energy and solve for R0, yielding a nucleus size near 12 femtometers and supporting Rutherford's model of a small nucleus.

Explore the evolution of the classical atomic theory, from Dalton and Thomson to Rutherford, Bohr, and Schrödinger, addressing spectra, stability, and the shift to quantum mechanics.

Explore atom models based on quantum mechanics, discuss two models, learn the basic principles, and introduce charge, mass, and spin as fundamental particle quantities.

Trace the evolution from Dalton's homogeneous spheres to Thomson's electron in a background, to Rutherford's nucleus and electrons, noting stability concerns and spectral lines guiding quantum mechanics and Schrödinger's model.

Explore how the photoelectric effect revealed quantum mechanics, showing photons with energy hf eject electrons and define kinetic energy, leading to Planck's constant and Bohr's atomic model.

Explore how Bohr's model explains discrete energy levels and photon transitions, improving the Rutherford picture, and why its stability fails without quantum theory.

Bohr's model is unstable because accelerating charges radiate energy (Larmor formula) per the Maxwell equations, causing orbit to shrink and the atom to spiral toward the nucleus, underscoring quantum mechanics.

Apply Sommerfeld quantization to determine the Bohr radius of the hydrogen atom's orbit, with angular momentum equal to hbar, and compare gravitational and electrostatic forces to find the radius.

Derive the Bohr radius for an orbiting electron using Sommerfeld quantization, compare gravity and electrostatic forces, and show why charge distribution yields a real atomic size around 0.5 angstrom.

Explore how the double-slit experiment reveals wave-particle duality, illustrating interference via a wave function and the role of measurement as in Schrödinger's cat thought experiment.

Explore how wave-particle duality for light and electrons leads to interference, while measurement disturbs momentum, enforcing Heisenberg’s uncertainty principle and shaping the quantum model of the atom.

Experience the quantum orbital model of the atom, where a probability cloud replaces orbits, described by the Schrödinger equation and the wave function with |Ψ|^2 density.

Explore the Schrodinger equation as the tool for describing quantum systems, apply it to the hydrogen atom, and derive orbitals and their energies from quantum numbers n, L, and M.

Explore the hydrogen 1s orbital by using its ground-state wave function to compute the electron’s average position and its average distance to the nucleus, using spherical coordinates.

Derive the average electron position using symmetry and spherical coordinates, showing a 3/2 a0 average distance from the nucleus and relating quantum results to the Bohr radius.

Define spin as a quantum mechanical property of electrons with two states: spin up and spin down, linking magnetic moments, Stern-Gerlach observations, and orbital filling via the Pauli exclusion principle.

Analyze the classical interpretation of spin, note its limitations for the electron, relate orbital and spin magnetic moments, and estimate the electron radius under a light-speed spin limit.

Estimate the electron radius from a classical spin model of a rotating charge. Link the magnetic moment to current, then bound the size via Compton wavelength and the uncertainty principle.

Pauli's exclusion principle for fermions states two electrons cannot share identical quantum numbers, so an orbital holds at most two with opposite spin, explaining periodic-table shell structure.

Explore the term diagram and electron configuration, covering quantum numbers, the Pauli principle, and how relativistic effects alter energy levels and the magic numbers of noble gases.

Apply Hund's rules to fill equivalent orbitals, maximizing spin and angular momentum under Pauli's principle. Illustrate with aluminum, silicon, and argon to show spin up preferences and orbital filling.

Trace the evolution from Dalton's atom to quantum mechanics, detailing electrons, nucleus, energy levels, wave functions, and the four fundamental interactions within the standard model.

Explore nuclear physics by examining protons and neutrons in the nucleus, initially treated as fundamental particles, and learn how quarks enable the strong interaction toward the Standard Model.

Explore the nucleus by studying protons and neutrons and the strong interaction that binds them to quarks and the Standard Model, showing they are not elementary.

Explore how the Thomson plum pudding model failed and Rutherford's gold foil experiments revealed a heavy nucleus. Trace how protons and neutrons form the nucleus and relate charge and mass.

Explore the proton, the first nucleus particle, with its mass, charge, and spin. Learn that it has a substructure of quarks and how this fits the standard model.

Explore how isotopes arise from Soddy and Thomson's 1913 experiments, showing neon can have different masses with the same charge, leading to the discovery of the neutron.

Explain how Porter and Chadwick discovered the neutron as a neutral particle with a mass near the proton, resolving mass gaps in isotopes. Note its zero charge and spin 1/2.

Classify nuclides by protons and neutrons using the atomic number Z and mass number A, and explore how isotopes and hydrogen variants differ in neutron count and mass.

Explore isobars, isotones, isodiaphers, and isomers, and learn how Z, protons, neutrons, and nucleons define isotopes and mirror nuclei in nuclear physics.

Investigate how neutron numbers affect atom stability and the existence of stable and unstable isotopes. See how the mass difference relates to binding energy, shaping stability.

Explore how e = m c squared links mass defect to binding energy and atomic stability, illustrated by uranium-238 calculations and iron-56 as the most stable per nucleon.

Explore quarks and the strong interaction that binds protons and neutrons into nuclei, and why most of the nucleon mass comes from gluons, sea quarks, and kinetic energy.

Explore how the strong interaction between quarks creates the nuclear force that binds protons and neutrons at about one femtometer, enabling nuclear stability through a residual attraction.

Balance attraction and Coulomb repulsion in a model that treats the nucleus as an incompressible liquid. Incorporate volume and surface energy terms, asymmetry and pairing terms to capture binding energy.

Quantify binding energy with the Bethe-Weizsäcker formula, summing volume, surface, Coulomb, asymmetry, and pairing. Highlight that coefficients are fitted to data and the model reveals stability.

Practice four steps to identify the most stable nuclide by maximizing binding energy with respect to Z using a simplified beta leitzinger formula, and analyze light versus heavy element stability.

This solution-focused lecture derives the ideal proton number by maximizing binding energy, and analyzes the binding energy per nucleon to identify the most stable nuclide, noting model limitations.

Identify why the liquid drop model shows systematic energy errors and how magic numbers reveal extra stability, motivating the nuclear shell model based on quantum mechanics.

The nuclear shell model, based on quantum mechanics, treats protons and neutrons separately, forming shells and explaining magic numbers, with spin-orbit coupling and a modified harmonic oscillator potential.

Explore how the nuclear shell model explains magic numbers, including double magic with both protons and neutrons, and compare with liquid drop and beta bicycle formulas, citing helium-4 and oxygen-16.

Use the nuclear shell model to refine beta formulas and explain magic numbers behind helium-4 and oxygen-16 stability, and predict islands of stability for future elements.

We introduced protons and neutrons, isotopes and isobars, discussed the liquid drop model, and explored magic numbers and the prospect of new elements in the future.

Explore how heavy nuclei decay via alpha, beta, and gamma processes and general radioactivity. See how these decays heat Earth's interior and support geothermal energy ideas with practical examples.

Explore radioactivity and nuclear decay, linking binding energy and mass defect via energy-mass equivalence to stability, and outline decay modes like alpha and beta, plus the nuclear chart.

Explore ionizing radiation types—alpha, beta, gamma, and neutrons—and how they ionize matter, and learn to quantify activity, exposure, and dose with becquerel, gray, and sievert.

Understand how radioactivity and ionizing radiation affect humans with the equivalent dose in sieverts and gray, using weighting factors for x rays, gamma, beta, alpha, protons, and neutrons.

Detect ionizing radiation with cloud chambers that visualize alpha-particle tracks in supersaturated alcohol vapors, and explore Geiger-Müller counters and x-ray fluorescence imaging for radiation measurement and bone visualization.

Explain alpha decay by presenting alpha particles as helium-4 nuclei emitted by heavy elements to reduce nuclear size toward stability, powered by quantum tunneling through the Coulomb barrier.

Beta decay converts a neutron to a proton with emission of an electron and a neutrino or antineutrino to conserve charge; neutrinos have tiny mass and spin 1/2.

Differentiate beta minus and beta plus decay, where neutrons turn into protons with an electron and antineutrino, or vice versa with a positron and neutrino, via the weak interaction.

The lecture demonstrates gamma decay as excited nuclides emit high-energy photons that ionize matter while relaxing to the ground state after alpha or beta decay, illustrated by caesium 137 isomers.

Explore electron capture and related decay processes, including beta decay and beta plus decay, with sodium-22 decaying to neon and energy carried away by a photon or neutrino.

Explore the exponential radioactive decay law by deriving the differential equation dn/dt = -P n and its exponential solution, and connect the decay probability P to the half-life tau1/2.

Explore decay chains in radioactive series, tracing alpha decays and occasional beta minus events that guide transitions toward stable lead or thallium across four chains.

Explore how alpha, beta, and gamma decay inside the earth heats the planet and enables geothermal energy potential. Look ahead to a wider outlook and the following two videos.

Explore geothermal energy by tracing heat from Earth's interior to the crust, and see how plate tectonics and heat from radioactive processes keep the planet hot.

Explore how Earth's geothermal energy arises from both primordial heat since the Big Bang and ongoing radioactive decay of uranium and thorium isotopes, with alpha and beta decays releasing heat.

Investigate how geothermal energy arises from radioactive heating in uranium and thorium decays, and how binding energy and mass-energy equivalence govern alpha decay in uranium-238.

Model uranium-238 decay as a decaying exponential, summing alpha and beta decays along the chain to lead, releasing 51.4 MeV per atom and about 12 terawatts from mantle uranium.

Practice calculating thorium-232 decay power by repeating the uranium-238 method, then compute energy per atom, energy per kilogram, and decay rate from the given half-life to estimate Earth's total power.

Calculate the thorium-232 decay chain energy by summing alpha decay energies to 42.66 MeV per atom. Estimate the energy density and Earth's total thorium power near 14 terawatts under equilibrium.

Complete the section on radioactive decay by detailing alpha, beta, and gamma processes and explain how they heat the earth's interior, revealing geothermal energy potential.

Learn how radiocarbon dating uses the C-14 to C-12 ratio and a 5700-year half-life, along with calibration curves, to determine the age of organic matter.

Explore nuclear decay and fission, including alpha emission and uranium splitting, and compare them with fusion as a way to release binding energy on Earth and in the sun.

Explains how nuclear fission splits heavy nuclei such as uranium-235 into more stable fragments, releasing energy as binding energy per nucleon increases and stability improves.

Investigate how uranium-235 fission occurs when struck by a neutron, producing barium-139 and krypton with neutrons released and energy as kinetic energy to heat water in power plants.

Calculate energy per kilogram for methane combustion, hydrogen combustion, and uranium-235 fission; compare the three scenarios.

Explore energy densities of hydrogen, natural gas, and uranium, noting hydrogen about 143 mj/kg and uranium fission around 82 tj/kg; splitting the atom offers enormous energy and is dangerous.

Explain how uranium-235 fission releases energy and produces neutrons that drive a chain reaction. Compare enriched uranium with natural uranium-238 to prevent runaway reactions and introduce the critical mass concept.

Explain how critical mass governs a nuclear chain reaction by balancing surface and volume effects, neutron leakage, and neutron deflection, from uranium-235 to uranium-238.

Explore fusion as merging light elements like hydrogen to harvest binding energy, and compare it with fission's energy release and the dangers and difficulties of fusion power on earth.

Explore nuclear fusion concepts by calculating sun energy from hydrogen into helium, understanding mass defect via E=mc^2, and estimating solar energy reach and global demand.

Discover how the sun's power from nuclear fusion arises from mass-energy conversion, estimate earth-bound power, and see why harvesting 0.01% could meet humanity's energy needs.

Explore solar fusion transforming hydrogen isotopes protium, deuterium, and tritium into helium, emitting positrons, neutrinos, and gamma rays, and how this process inspires fusion on Earth for energy.

This lecture explains why replicating stellar fusion on earth favors deuterium-tritium fusion despite extreme temperature demands, due to higher energy yield, while addressing density and size limits and neutron-related radioactivity.

Examine deuterium-tritium fusion and the Lawson criterion, linking high temperature, density, and confinement time to overcome losses and achieve net energy.

Explore the challenges of achieving cost-efficient nuclear fusion on Earth, focusing on tokamak magnetic confinement, the Lawson criterion, and the path toward net energy gain.

Breed tritium for fusion by neutron irradiation of lithium or boron, but tritium's radioactivity and scarcity pose challenges; high-energy neutrons heat shields that become radioactive waste.

Fusion energy offers climate-neutral power with no carbon emissions and abundant hydrogen, plus non-critical reactions and no long-lived radioactive waste, but high costs and radioactive shield components remain challenges.

Summarize the core ideas of nuclear fusion and fission, tied to binding energy curves and energy release in heavy-element splitting and light-element fusion, building on the nucleus model and radioactivity.

Discover how short-lived technetium enables gamma imaging and targeted radionuclide therapy with fluorine-based PET tracers, iodine, yttrium, and cesium.

Explore how quarks compose protons and neutrons, introducing the standard model of elementary particles, including electrons, and note that gravity lies outside the four fundamental interactions.

Explore the standard model, protons and neutrons as up and down quarks with color, and how strong, electromagnetic, and weak forces create bound states and antiparticles, including neutrinos.

Classify the standard model into quarks, leptons, gauge bosons, and scalar bosons, and contrast fermions and bosons by spin and the antiparticle concept.

Explore the six quark flavors across three generations, their spin-1/2 fermion nature, and how mass, charge, and color charge enable strong, weak, electromagnetic, and gravitational interactions.

Explore how quarks carry color charge and combine into colorless hadrons, forming mesons (quark–antiquark pairs), baryons (three quarks), and antibaryons.

Learn about leptons—electron, muon, tau—and their neutrinos, including antiparticles and the three generations with distinct masses and charges. See how weak interaction governs their decays and generation structure.

Explore how fermions and bosons shape the standard model, where spin, Pauli exclusion principle, and field quanta define matter and force carriers like the photon, gluon, and W/Z bosons.

Describe gauge bosons as carriers of fundamental forces, from the photon mediating electromagnetism to the gluon of the strong force and the W and Z bosons of the weak interaction.

Summarize weak interaction, its flavor dependence and weak isospin, with Z and W bosons mediating processes. Explain chirality and electroweak theory, and its role in beta decay and solar fusion.

Explore Higgs boson as a scalar from the Higgs field that gives mass to W and Z bosons via the Higgs mechanism. Note the standard model limits and gravity's absence.

Explore the standard model's limitations, including gravity's absence and potential extra scalar bosons, and probe unification, matter-antimatter asymmetry, and possible extra generations.

Explore theories like quantum gravity, string theory, and the theory of everything, and examine how a grand unifying theory could describe gravity, electromagnetism, weak, and strong interactions at high energies.

Review the standard model’s elementary particles, mass, charge, and spin, and the four fundamental interactions, noting that gravity lies outside the model and future theories may unify them.

Explore the Schrödinger equation and the fundamentals of quantum mechanics, solving the particle in a box and the hydrogen atom to derive energy levels and orbitals.

Motivate and derive the Schrödinger equation by uniting wave and particle pictures and energy, momentum, and the wavefunction, then explore Hamiltonian, time dependence, and hydrogen energy levels.

Explore what complex numbers are, why we use them to solve quadratics with real and imaginary zeros, and how the complex plane encodes real and imaginary parts.

Solve the particle in a box to illustrate the Schrodinger equation, with zero potential inside and infinite walls, yielding discrete energy levels and photon emission or absorption.

Solve the particle in a box via the stationary Schrödinger equation with zero interior and infinite exterior potential, derive the energy spectrum, and normalize the wave function using boundary conditions.

The particle in a box shows a discrete energy spectrum with levels scaling as n squared, and spacings shrink as the box enlarges, approaching a quasi-continuous spectrum.

Explore the hydrogen atom by solving the Schrödinger equation with a Coulomb 1/r potential, deriving energy levels and wave functions for orbitals s, p, and d in spherical coordinates.

Solve the hydrogen atom via the stationary Schrödinger equation with a Coulomb potential. Separate variables in spherical coordinates to obtain radial and angular equations, yielding three one-dimensional problems.

The lecture solves the angular part of the hydrogen atom, deriving the phi and theta equations and introducing l and m quantum numbers with associated Legendre polynomials and spherical harmonics.

Solve the radial equation of the hydrogen atom by transforming the Schrödinger equation to an effective one-dimensional form, introduce Laguerre functions, derive quantum numbers and the energy spectrum.

Discover how the hydrogen atom's energy levels arise from solving the Schrodinger equation in spherical coordinates, yielding E_n = -13.6 eV / n^2 and orbitals labeled by L and M.

Derive energy levels and orbitals by analytically solving the Schrodinger equation from scratch, without computers. Rewatch or explore the full course on this website about quantum mechanics for deeper background.

Solve the particle in a ring by applying the Schrödinger equation in polar coordinates, derive eigenfunctions and eigenvalues, impose periodic boundary conditions, and determine quantum numbers and normalization.

Derives eigenfunctions and eigenvalues for a particle on a ring, linking benzene’s circular electron motion to a quasi one-dimensional Schrödinger problem with periodic boundary conditions and degenerate energy levels.

Explore the spin concept from fermions to bosons, linking half-integer spins to Pauli exclusion and to relativistic quantum mechanics and statistical physics in the standard model context.

Explore how electron spin arises from Stern-Gerlach experiments and Pauli's phenomenological approach, introducing a two-component wavefunction for spin up and down and Pauli matrices to couple spin with magnetic fields.

Explore how special relativity reconciles quantum mechanics with the Dirac equation, explaining time dilation, length contraction, Lorentz factor, relativistic mass, and energy-mass relations in high-energy motion.

Derive the relativistic energy–momentum relation from special relativity, showing E^2 = p^2 c^2 + m^2 c^4, and how positive and negative solutions reveal particles and antiparticles.

Practice deriving the first relativistic energy correction by Taylor expanding the energy–momentum relation to second order, yielding E ≈ m c^2 + p^2/(2m) and identifying the rest and kinetic terms.

Expand relativistic energy around zero momentum by calculating E(p) at p=0 and its derivatives, revealing rest energy m c^2 and the p^2/M classical kinetic energy term, plus relativistic corrections.

Introduce Dirac equation as the relativistic quantum description of electrons and positrons with a four-component spinor. Fulfills the relativistic energy momentum relation and couples to the four-potential for electromagnetic fields.

Derive relativistic corrections to hydrogen from a one over c^2 Dirac expansion. Include spin-orbit coupling and the Darwin term, revealing L and J-dependent fine structure and photon spectra.

Relativistic corrections shift hydrogen energy levels and split S and P states by total angular momentum J, with spin-orbit and Darwin terms, explaining 4s before 3d ordering in periodic table.

Explore how nuclear spin arises from protons and neutrons in the shell model, with spin-orbit coupling, magic numbers, and Hund's rules illustrated by hydrogen, deuterium, lithium, and oxygen.

Explore hyperfine structure as tiny corrections to electron energy levels due to nuclear spin, spin-orbit coupling, and hydrogen's F-split states driven by total angular momentum J and nuclear spin.

Explore how spin distinguishes fermions and bosons and how Pauli's exclusion principle shapes statistical physics, deriving occupation numbers and the Fermi-Dirac and Bose-Einstein distributions from the partition function.

Explore fermions under Pauli exclusion, showing a 0 or 1 occupation, derive the Fermi-Dirac distribution with chemical potential, and explain temperature broadening from zero to finite temperatures.

Explore Bose-Einstein statistics for bosons, deriving the occupation number summing to infinity, using a geometric series and derivative with respect to chemical potential, and compare to fermions and Boltzmann statistics.

Explore the classical limit of quantum statistics by deriving the Boltzmann distribution from the occupation functions of fermions and bosons, and compare Fermi-Dirac, Bose-Einstein, and Boltzmann cases.

The lecture explains spin as a fundamental quantity that characterizes elementary and compound particles, including protons and neutrons, and emphasizes that understanding spin requires calculation rather than intuition.

Explore how atoms combine to form molecules, building on nuclei, atoms, electrons, and energy states, and learn the fundamentals of molecular formation.

Explore how atoms bind via the lennard-jones potential, with pauli repulsion at short range, van der waals forces including the london force, and a minimum that yields harmonic-oscillator-like vibrations.

Two hydrogen atoms form bonding and antibonding molecular orbitals through linear combination of atomic orbitals, producing lower and higher energy states labeled sigma and sigma*.

Explore how multiple atoms bind to form molecules, linking molecular physics to atomic physics as you learn to describe and understand these new objects.

Discover how billions of atoms form periodic solids and how solid-state physics, or condensed matter physics, provides theoretical methods to describe solids from atomic building blocks.

Explore how adding atoms forms band structure and dispersion in solids. Relate Fermi level and band gaps to metals, semiconductors, and insulators.

Use tight binding to compute graphene's band structure from a two-atom unit cell, derive hopping terms and the Hamiltonian, and reveal massless Dirac fermions with a linear energy–momentum relation.

Explore quasi particles as effective descriptions in solids, including electrons with an effective mass, and bosons like phonons and magnons, illustrating collective excitations and transport phenomena.

Conclude the section on solid state physics by highlighting iron's atoms arranged periodically, enabling easier descriptions. Explain how atomic periodicity simplifies modeling in solid state physics and condensed matter physics.

Congratulations on completing the course and reflecting on the learning journey, while enjoying the exercises and quizzes. Explore my other courses, including quantum mechanics, and share a review.