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DP IB Physics: SL

Revision Notes

Home / IB / Physics: SL / DP / Revision Notes / 7. Atomic, Nuclear & Particle Physics / 7.3 The Structure of Matter / 7.3.4 Particle Conservation Laws


7.3.4 Particle Conservation Laws


Particle Conservation Laws

Charge

  • Electric charge must be conserved during particle interactions
    • This means charge must have the same value overall before and after the interaction

  • Charge is found in quarks, leptons and exchange particles and their anti-matter counterparts

Baryon Number

  • The baryon number, B, is the number of baryons in an interaction
  • B depends on whether the particle is a baryon, anti-baryon or neither
    • Baryons have a baryon number B = +1
    • Anti-baryons have a baryon number B = –1
    • Particles that are not baryons have a baryon number B = 0

  • Baryon number is a quantum number and is conserved in all interactions
    • This is one of the indicators for whether an interaction is able to occur or not

Lepton number

  • The lepton number, L, is the number of leptons in an interaction
  • L depends on whether the particle is a lepton, anti-lepton or neither
    • Leptons have a lepton number L = +1
    • Anti-leptons have a lepton number L = –1
    • Particles that are not leptons have a lepton number L = 0

  • Lepton number is a quantum number and is conserved in all interactions
    • This is one of the indicators for whether an interaction is able to occur or not

Conservation Laws

  • All particle interactions must obey a set of conservation laws. These are conservation of:
    • Charge, Q
    • Baryon number, B
    • Lepton Number, L
    • Strangeness, S
    • Energy (or mass-energy)
    • Momentum

  • However, strangeness does not need to be conserved in weak interactions. It can change by either 0, +1 or –1
  • Quantum numbers such as Q, B, L and S can only take discrete values (ie. 0, +1, –1, 1/2)
  • To know whether a particle interaction can occur, check whether each quantum number is equal on both sides of the equation
    • If even one of them, apart from strangeness in weak interactions, is not conserved then the interaction cannot occur

Conservation Laws Table, downloadable AS & A Level Physics revision notes

Example of a working out what is conserved in Kaon decay. This decay must be through the weak interaction since S is not conserved

Strangeness

  • Strangeness, S, like baryon and lepton number, is a quantum number
  • Strangeness is conserved in every interaction except the weak interaction
  • This means that strange particles are always produced in pairs (e.g. K+ and K–)
  • S depends on whether the particle contains a strange quark, anti-strange quark, or no strange quarks
    • Particles with an anti-strange quark have S = +1
    • Particle with a strange quark have S = –1
    • Particles with no strange quark have S = 0

Strangeness, downloadable AS & A Level Physics revision notes

Only particles with a strange or anti-strange quark have a strangeness of +1 or –1

  • Strangeness can change by 0, +1 or –1 in weak interactions

Strange Particles

  • Strange particles are particles that include a strange or anti-strange quark
  • An example of these are kaons
  • Strange particles always:
    • Are produced through the strong interaction
    • Decay through the weak interaction

  • An example of a kaon production could be:

Strong Interaction Kaons, downloadable AS & A Level Physics revision notes

Kaons are produced through the strong interaction. This is shown by the gluon exchange particle.

  • An example of kaon decay could be:

Weak Interaction Kaons, downloadable AS & A Level Physics revision notes

Kaons decay via the weak interaction. This is shown by the W+ boson.

Worked Example

The lambda nought particle Λ0 is has a quark composition uds.

Show, in terms of the conservation of charge, strangeness, baryon number and lepton number whether the following interaction is permitted:2.3.5 Conservation Laws Worked Example

Step 1: Determine conservation of charge, Q

    • The Λ0 has a charge of 0
    • The pion π– has a charge of –1
    • The positron e+ has a charge of +1
    • The electron neutrino νe has a charge of 0

0 = –1 + 1 + 0

    • Therefore, charge is conserved

Step 2: Determine conservation of strangeness, S

    • Λ0 has an s quark, so must have a strangeness of –1
    • None of the particles on the right hand side of the decay has a strange quark

–1 = 0 + 0 + 0

    • Therefore, strangeness is not conserved

Step 3: Determine conservation of baryon number, B

    • Λ0 is a baryon since it has 3 quarks, so must have a baryon number of +1
    • The pion π– is a meson so has a baryon number 0
    • The positron is a lepton so has a baryon number 0
    • The electron neutrino νe is a lepton so has a baryon number 0

+1 = 0 + 0 + 0

    • Therefore, baryon number is not conserved

Step 4: Determine conservation of lepton number, L

    • Λ0 is a baryon, so must have a lepton number of 0
    • The pion π– is a meson so has a lepton number of 0
    • The positron e+ is an anti-lepton so has a lepton number of –1
    • The electron neutrino νe is a lepton so has a lepton number of +1

0 = 0 + (–1) + 1

    • Therefore, lepton number is conserved

Step 5: Conclusion

    • Since the baryon number is not conserved, this interaction is not permitted

Worked Example

The equation for β– decay is2.3.3 Beta Minus Equation

Using the quark model of beta decay, prove that the charge is conserved in this decay.

Worked example - beta decay quarks, downloadable AS & A Level Physics revision notes

Worked Example

The sigma baryon has a quark structure of suu. It decays to produce a proton and pion as shown in the equation below2.2.6 Sigma Baryon Decay EquationProve that this decay is via the weak interaction.

Step 1: Determine the strangeness, S of each particle

    • Since sigma baryon has one s quark, it has S = –1
    • The proton and pion has no strange particles, so they have S = 0

Step 2: Determine strangeness, S on both sides of the equation

    • The sigma baryon has a S = –1 but the meson and proton have a S = 0

–1 = 0 + 0

Step 3: Comment on the conservation of strangeness

    • Since S is not conserved on both sides of the decay equation (only changed by –1), this decay is via the weak interaction
    • This is because S is conserved in all other types of interaction (strong and EM), but isn't always conserved in weak interactions



  • 1. Measurement & Uncertainties
    • 1.1 Measurements in Physics
      • 1.1.1 SI Units
        • 1.1.2 Using Scientific Notation
          • 1.1.3 Estimating Physical Quantities
          • 1.2 Uncertainties & Errors
            • 1.2.1 Random & Systematic Errors
              • 1.2.2 Calculating Uncertainties
                • 1.2.3 Determining Uncertainties from Graphs
                • 1.3 Vectors & Scalars
                  • 1.3.1 Vector & Scalar Quantities
                    • 1.3.2 Combining & Resolving Vectors
                      • 1.3.3 Solving Vector Problems
                    • 2. Mechanics
                      • 2.1 Motion
                        • 2.1.1 Distance & Displacement
                          • 2.1.2 Speed & Velocity
                            • 2.1.3 Acceleration
                              • 2.1.4 Graphs Describing Motion
                                • 2.1.5 Uniform Acceleration
                                  • 2.1.6 Acceleration of Free Fall Experiment
                                    • 2.1.7 Projectile Motion
                                      • 2.1.8 Terminal Speed
                                      • 2.2 Forces
                                        • 2.2.1 Free-Body Diagrams
                                          • 2.2.2 Newton’s First Law
                                            • 2.2.3 Newton’s Second Law
                                              • 2.2.4 Newton’s Third Law
                                                • 2.2.5 Applying Newton’s Laws of Motion
                                                  • 2.2.6 Friction
                                                  • 2.3 Work, Energy & Power
                                                    • 2.3.1 Kinetic Energy
                                                      • 2.3.2 Gravitational Potential Energy
                                                        • 2.3.3 Elastic Potential Energy
                                                          • 2.3.4 Work Done
                                                            • 2.3.5 Power
                                                              • 2.3.6 Principle of Conservation of Energy
                                                                • 2.3.7 Efficiency
                                                                • 2.4 Momentum & Impulse
                                                                  • 2.4.1 Force & Momentum
                                                                    • 2.4.2 Impulse
                                                                      • 2.4.3 Conservation of Linear Momentum
                                                                        • 2.4.4 Collisions & Explosions
                                                                      • 3. Thermal Physics
                                                                        • 3.1 Thermal Concepts
                                                                          • 3.1.1 Solids, Liquids & Gases
                                                                            • 3.1.2 Temperature
                                                                              • 3.1.3 Internal Energy
                                                                                • 3.1.4 Specific Heat Capacity
                                                                                  • 3.1.5 Specific Latent Heat
                                                                                    • 3.1.6 Phase Change
                                                                                      • 3.1.7 Investigating Thermal Energy
                                                                                      • 3.2 Modelling a Gas
                                                                                        • 3.2.1 Ideal Gas Laws
                                                                                          • 3.2.2 Ideal Gas Equation
                                                                                            • 3.2.3 Kinetic Model of an Ideal Gas
                                                                                              • 3.2.4 Mole Calculations
                                                                                                • 3.2.5 Investigating Gas Laws
                                                                                              • 4. Waves
                                                                                                • 4.1 Oscillations
                                                                                                  • 4.1.1 Properties of Oscillations
                                                                                                    • 4.1.2 Simple Harmonic Oscillations
                                                                                                      • 4.1.3 SHM Graphs
                                                                                                        • 4.1.4 Energy in SHM
                                                                                                        • 4.2 Travelling Waves
                                                                                                          • 4.2.1 Properties of Waves
                                                                                                            • 4.2.2 Transverse & Longitudinal Waves
                                                                                                              • 4.2.3 Electromagnetic Waves
                                                                                                                • 4.2.4 Sound Waves
                                                                                                                • 4.3 Wave Characteristics
                                                                                                                  • 4.3.1 Wavefronts
                                                                                                                    • 4.3.2 Amplitude & Intensity
                                                                                                                      • 4.3.3 Superposition
                                                                                                                        • 4.3.4 Polarisation
                                                                                                                          • 4.3.5 Malus’s Law
                                                                                                                          • 4.4 Wave Behaviour
                                                                                                                            • 4.4.1 Reflection, Refraction & Transmission
                                                                                                                              • 4.4.2 Reflection
                                                                                                                                • 4.4.3 Refraction
                                                                                                                                  • 4.4.4 Determining Refractive Index
                                                                                                                                    • 4.4.5 Single-Slit Diffraction
                                                                                                                                      • 4.4.6 Interference & Path Difference
                                                                                                                                        • 4.4.7 Double-Slit Equation
                                                                                                                                        • 4.5 Standing Waves
                                                                                                                                          • 4.5.1 The Nature of Standing Waves
                                                                                                                                            • 4.5.2 Nodes & Antinodes
                                                                                                                                              • 4.5.3 Boundary Conditions for Standing Waves
                                                                                                                                                • 4.5.4 Harmonics
                                                                                                                                              • 5. Electricity & Magnetism
                                                                                                                                                • 5.1 Electric Fields
                                                                                                                                                  • 5.1.1 Charge & Current
                                                                                                                                                    • 5.1.2 Drift Speed
                                                                                                                                                      • 5.1.3 Potential Difference & DC
                                                                                                                                                        • 5.1.4 Electric Fields
                                                                                                                                                          • 5.1.5 Coulomb’s Law
                                                                                                                                                          • 5.2 Heating Effect of Electric Currents
                                                                                                                                                            • 5.2.1 Circuits
                                                                                                                                                              • 5.2.2 Resistance & Resistors
                                                                                                                                                                • 5.2.3 Kirchhoff’s Circuit Laws
                                                                                                                                                                  • 5.2.4 I-V Characteristics
                                                                                                                                                                    • 5.2.5 Resistivity
                                                                                                                                                                      • 5.2.6 Investigating Resistivity
                                                                                                                                                                        • 5.2.7 Series & Parallel Circuits
                                                                                                                                                                          • 5.2.8 Heating Effect of Current
                                                                                                                                                                            • 5.2.9 Potential Divider Circuits
                                                                                                                                                                            • 5.3 Electric Cells
                                                                                                                                                                              • 5.3.1 Primary & Secondary Cells
                                                                                                                                                                                • 5.3.2 Investigating Electric Cells
                                                                                                                                                                                  • 5.3.3 Terminal Potential Difference
                                                                                                                                                                                    • 5.3.4 Electromotive Force & Internal Resistance
                                                                                                                                                                                    • 5.4 Magnetic Effects of Electric Currents
                                                                                                                                                                                      • 5.4.1 Magnetic Fields
                                                                                                                                                                                        • 5.4.2 Magnetic Force on a Charge
                                                                                                                                                                                          • 5.4.3 Magnetic Force on a Current-Carrying Conductor
                                                                                                                                                                                            • 5.4.4 Solving Problems Involving Magnetic Forces
                                                                                                                                                                                          • 6. Circular Motion & Gravitation
                                                                                                                                                                                            • 6.1 Circular Motion
                                                                                                                                                                                              • 6.1.1 Circular Motion
                                                                                                                                                                                                • 6.1.2 Centripetal Force
                                                                                                                                                                                                  • 6.1.3 Centripetal Acceleration
                                                                                                                                                                                                    • 6.1.4 Applications of Circular Motion
                                                                                                                                                                                                    • 6.2 Newton’s Law of Gravitation
                                                                                                                                                                                                      • 6.2.1 Newton’s Law of Gravitation
                                                                                                                                                                                                        • 6.2.2 Circular Orbits
                                                                                                                                                                                                          • 6.2.3 Gravitational Field Strength
                                                                                                                                                                                                        • 7. Atomic, Nuclear & Particle Physics
                                                                                                                                                                                                          • 7.1 Discrete Energy & Radioactivity
                                                                                                                                                                                                            • 7.1.1 Discrete Energy Levels
                                                                                                                                                                                                              • 7.1.2 Calculating Discrete Energies
                                                                                                                                                                                                                • 7.1.3 Emission & Absorption Spectrum
                                                                                                                                                                                                                  • 7.1.4 Isotopes & Radioactive Decay
                                                                                                                                                                                                                    • 7.1.5 Background Radiation
                                                                                                                                                                                                                      • 7.1.6 Alpha, Beta & Gamma Particles
                                                                                                                                                                                                                        • 7.1.7 Decay Equations
                                                                                                                                                                                                                          • 7.1.8 Half-Life
                                                                                                                                                                                                                            • 7.1.9 Investigating Half-Life
                                                                                                                                                                                                                            • 7.2 Nuclear Reactions
                                                                                                                                                                                                                              • 7.2.1 Atomic Mass Unit
                                                                                                                                                                                                                                • 7.2.2 Mass Defect & Nuclear Binding Energy
                                                                                                                                                                                                                                  • 7.2.3 Nuclear Fission & Fusion
                                                                                                                                                                                                                                    • 7.2.4 Binding Energy per Nucleon Curve
                                                                                                                                                                                                                                    • 7.3 The Structure of Matter
                                                                                                                                                                                                                                      • 7.3.1 Discovery of the Nucleus
                                                                                                                                                                                                                                        • 7.3.2 Quarks & Leptons
                                                                                                                                                                                                                                          • 7.3.3 Hadrons, Baryons & Mesons
                                                                                                                                                                                                                                            • 7.3.4 Particle Conservation Laws
                                                                                                                                                                                                                                              • 7.3.5 Fundamental Forces
                                                                                                                                                                                                                                                • 7.3.6 Feynman Diagrams & Confinement
                                                                                                                                                                                                                                                  • 7.3.7 The Standard Model of Particle Physics
                                                                                                                                                                                                                                                • 8. Energy Production
                                                                                                                                                                                                                                                  • 8.1 Energy Sources
                                                                                                                                                                                                                                                    • 8.1.1 Specific Energy
                                                                                                                                                                                                                                                      • 8.1.2 Sankey Diagrams
                                                                                                                                                                                                                                                        • 8.1.3 Primary & Secondary Energy Sources
                                                                                                                                                                                                                                                          • 8.1.4 Energy Resources
                                                                                                                                                                                                                                                            • 8.1.5 Energy Generation
                                                                                                                                                                                                                                                              • 8.1.6 Safety Issues in Nuclear Power
                                                                                                                                                                                                                                                              • 8.2 Thermal Energy Transfer
                                                                                                                                                                                                                                                                • 8.2.1 Conduction, Convection & Thermal Radiation
                                                                                                                                                                                                                                                                  • 8.2.2 Black-Body Radiation
                                                                                                                                                                                                                                                                    • 8.2.3 The Solar Constant, Albedo & Emissivity
                                                                                                                                                                                                                                                                      • 8.2.4 The Greenhouse Effect
                                                                                                                                                                                                                                                                        • 8.2.5 Earth's Surface–Atmosphere System
                                                                                                                                                                                                                                                                      Katie Moon

                                                                                                                                                                                                                                                                      Author: Katie

                                                                                                                                                                                                                                                                      Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.


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