Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Nuclear and particle physics → Particle physics ↓


Quarks and Leptons


In the world of particle physics, everything around us is made up of fundamental particles. These are the building blocks from which atoms and consequently all matter are made. The most important categories of these particles include quarks and leptons.

Understanding the basics

To understand the nature of matter, scientists have developed a theory called the Standard Model of particle physics. It describes how fundamental particles and forces interact.

Quarks and leptons are the two fundamental particles described by the Standard Model. Both are considered elementary particles, meaning they are not made up of smaller particles. Let's take a deeper look at what these particles are and why they are so important.

Quarks

Quarks are the fundamental particles that make up the building blocks of protons and neutrons, which you can find in the nucleus of an atom.

There are six types (or "flavors") of quarks:

  • up (u)
  • down (d)
  • Attraction (c)
  • Strange
  • top(T)
  • down (b)

Each quark has a fractional electric charge. For example, an up quark has a charge of +2/3 e, and a down quark has a charge of -1/3 e, where e represents the elementary charge.

Quark charge:
  Up: +2/3 E
  Bottom: -1/3 E
  Attraction: +2/3 E
  Odd: -1/3 e
  Top: +2/3 E
  Bottom: -1/3 E

Quarks combine to form hadrons, the most stable of which are protons and neutrons. A proton is made of two up quarks and one down quark, giving it a net charge of +1 e:

Proton = Ud -> (2/3 e + 2/3 e - 1/3 e) = +1 e

The neutron is made of one up quark and two down quarks, giving it a neutral charge:

Neutron = udd -> (2/3 e - 1/3 e - 1/3 e) = 0
You You D

Visual depiction of the quark structure of the proton.

Leptons

Quarks are the building blocks of matter, while leptons are fundamental particles that do not experience strong forces. Instead, leptons are affected by electromagnetic, weak, and gravitational forces.

There are six types of leptons and they come in pairs:

  • Electron (e) and electron neutrino (νe)
  • Muon (μ) and muon neutrino (νμ)
  • Tau (τ) and tau neutrino (ντ)

Charged leptons (electron, muon, tau) have a charge of -1 e. Neutrinos are neutral particles with very small masses, which interact only via weak forces.

Electrons are the leptons we encounter every day, as they orbit the nuclei of atoms, facilitating chemical bonds and electricity.

Lepton charge:
  Electron: -1 e
  Muon: -1 e
  Tau: -1E
  Neutrinos: 0
E νe μ

A visual depiction of some leptons, showing the electron, electron neutrino, and muon.

Mixed particles

Quarks combine to form composite particles called hadrons. The two main categories are baryons and mesons.

Baryons

Baryons are made of three quarks. Protons and neutrons are the most well-known baryons. The arrangement of the quarks obeys the rule that the net fractional charge must be a whole number.

Mesons

Mesons consist of a quark and an antiquark pair. They play an important role in the forces between nucleons in the nucleus.

Why Why Mason

This SVG shows a quark and antiquark forming a meson.

Forces and interactions

Quarks and leptons interact via the known fundamental forces:

  • Electromagnetic force: Affects charged particles such as electrons and quarks.
  • Weak Nuclear Force: Responsible for radioactive decay, affects neutrinos and quarks.
  • Strong nuclear force: Holds the quarks together within protons and neutrons.
  • Gravitational force: The weakest but affects particles that have mass.

Each interaction is governed by particles known as exchange or gauge bosons. These include the photon, the W, and Z bosons, and the gluon.

Role of gluons

Gluons mediate the strong forces that bind together the quarks inside protons and neutrons, collectively known as nucleons. Without gluons, the structure of an atom's nucleus would collapse.

Yes Yes

A visual representation of the gluons that facilitate the strong force between quarks.

Conclusion

Quarks and leptons are the essence of matter in the universe. Understanding these particles and their interactions gives us insight into the fundamental workings of the universe. The Standard Model, though not perfect, provides a robust framework for predicting and explaining the behavior of particles at the smallest scales.

Quarks, with their different flavors, combine in interesting ways to form the particles we see. Leptons, especially electrons, are important for understanding atomic structure and chemical reactions.


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