Particles and Nuclear Structure
| 7 Particles and Nuclear Structure Learners should be able to demonstrate and apply their knowledge and understanding of: |
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| a) | The idea that matter is composed of quarks and leptons and that there are three generations of quarks and leptons, although no questions will be set involving second or third generations
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| b) | The idea that antiparticles exist for the particles given in the table above, that the properties of an antiparticle are identical to those of its corresponding particle apart from having opposite charge, and that particles and antiparticles annihilate | ||||||||||||||||||||
| c) | Symbols for a positron and for antiparticles of quarks and hadrons | ||||||||||||||||||||
| d) | The idea that quarks and antiquarks are never observed in isolation, but are bound into composite particles called hadrons, or three types of baryons (combinations of 3 quarks), or antibaryons (combinations of 3 antiquarks) or mesons (quark-antiquark pairs) | ||||||||||||||||||||
| e) | The quark compositions of the neutron and proton | ||||||||||||||||||||
| f) | How to use data in the table on page 20 to suggest the quark make-up of less well-known first-generation baryons and of charged pions | ||||||||||||||||||||
| g) | The properties of the four forces or interactions experienced by particles as summarized in the table below
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| h) | How to apply conservation of charge, lepton number and baryon number (or quark number) to given simple reactions | ||||||||||||||||||||
| i) | The idea that neutrino involvement and quark flavour changes are exclusive to weak interactions | ||||||||||||||||||||
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a) The Structure of Matter: Quarks and Leptons
- Modern particle physics describes matter as being composed of fundamental particles, which cannot be broken down further. These particles belong to two main families: quarks and leptons. These fundamental particles form the building blocks of all matter in the universe.
- ⇒ Leptons
- Leptons are a family of particles that do not experience the strong nuclear force but interact via the weak nuclear force, electromagnetic force (if charged), and gravity. There are six leptons, divided into three generations, but we will focus on the first generation, which consists of:
- – The electron (e−): A charged particle with a negative electric charge of −1e.
- – The electron neutrino ( [math][/math]): A neutral particle with almost no mass.
- ⇒ Properties of Leptons:
- 1. Electron (e−):
- – Charge: −1 (negative)
- – Mass: [math]9.109 × 10^{-31}[/math](lightweight compared to most particles)
- – The electron is stable and commonly found in atoms, orbiting the nucleus
- – It interacts electromagnetically and weakly.
- 2. Electron Neutrino ([math]V_e[/math] ):
- – Charge: 0 (neutral).
- – Mass: Extremely small, but not zero (on the order of less than 1 eV/c²)
- – The electron neutrino rarely interacts with matter due to its lack of charge and weak interactions, making it difficult to detect.
- Leptons also have antiparticles, such as the positron (e+), which is the electron’s positively charged counterpart.
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⇒ Quarks
- Quarks are fundamental particles that combine to form hadrons, such as protons and neutrons. Unlike leptons, quarks experience the strong nuclear force, which binds them together inside protons and neutrons. There are six types of quarks, also divided into three generations. For the first generation, we focus on:
- – The up quark (u).
- – The down quark (d).
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⇒ Properties of Quarks:
- 1. Up Quark (u):
- – Charge:[math]+\frac{2}{3}e[/math] (positive)
- – Found in protons and neutrons
- – Mass: Approximately 2.2 MeV/c2
- 2. Down Quark (d):
- – Charge: [math]- \frac{1}{3}e[/math](negative).
- – Found in protons and neutrons.
- – Mass: Approximately 4.7 MeV/c2
- Figure 1 Quarks and leptons
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⇒ Quarks in Protons and Neutrons:
- Protons (p) are made of two up quarks and one down quark (uud).
- – Total charge:
- [math]+ \frac{2}{3} + \frac{2}{3} – \frac{1}{3} = 1e[/math]
- Neutrons (n) are made of one up quark and two down quarks (udd).
- – Total charge:
- [math]+ \frac{2}{3} – \frac{1}{3} – \frac{1}{3} = 0e[/math]
- Quarks are never found alone in nature due to a property called confinement; they are always bound together to form composite particles (e.g., protons, neutrons, or mesons).
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⇒ Three Generations of Quarks and Leptons
- Although this explanation focuses on the first generation, it is important to note that there are two additional generations of heavier quarks and leptons:
- 1. Second Generation:
- – Leptons: Muon (μ−), Muon neutrino ([math]ν_μ[/math]).
- – Quarks: Charm (c), Strange (s).
- 2. Third Generation:
- – Leptons: Tau (τ−), Tau neutrino ( [math]ν_τ[/math]).
- – Quarks: Top (t), Bottom (b).
- These higher generations are more massive and unstable, decaying quickly into first-generation particles.
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(b) Antiparticles: Properties and Annihilation
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⇒ Antiparticles
- Antiparticles are counterparts to regular particles, sharing the same mass and other properties but having the opposite charge and quantum numbers (such as baryon number or lepton number). For the particles in the table:
| Particle | Antiparticle | Charge (e) |
|---|---|---|
| Electron (e−) | Positron (e+) | +1 |
| Electron neutrino ([math]V_e[/math] ) | Electron antineutrino ([math]\bar{V_e}[/math] ) | 0 |
| Up quark (u) | Up-antiquark ( [math]\bar{u}[/math]) | [math]- \frac{2}{3}[/math] |
| Down quark (d) | Down antiquark ( [math]\bar{d}[/math]) | [math]+\frac{1}{3}[/math] |
- Figure 2 Antiparticles
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⇒ Annihilation of Particles and Antiparticles
- When a particle and its corresponding antiparticle meet, they annihilate each other, converting their mass into energy, often in the form of photons or other particles. This process is described by Einstein’s equation
- [math]E = mc^2[/math]
- – For example:
- An electron and positron annihilate as:
- [math]e^+ + e^- \to \gamma + \gamma[/math]
- (two photons are produced).
- Annihilation is fundamental to processes like pair production in particle physics and plays a role in phenomena like gamma-ray bursts and energy generation in particle accelerators.
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(c) Symbols for Positrons and Antiparticles
- 1. Positron ([math]e^+[/math]): The antiparticle of the electron ([math]e^-[/math] ).
- 2. Antiquarks:
- – Up antiquark:[math]\bar{u}[/math]
- – Down antiquark:[math]\bar{d}[/math]
- 3. Antiparticles of Hadrons:
- – Antiproton ([math]\bar{p}[/math] ): Composed of two up antiquarks and one down antiquark ([math]\bar{uud}[/math] )
- – Antineutron ( [math]\bar{n}[/math]): Composed of one up antiquark and two down antiquarks ( [math]\bar{udd}[/math]).
- These symbols indicate that antiparticles are notated with a bar over the corresponding particle’s symbol (e.g.[math]\bar{u}[/math], for the up antiquark).
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(d) Quarks and Antiquarks in Composite Particles
- Quarks and antiquarks cannot exist alone due to quark confinement. Instead, they are bound together by the strong nuclear force to form composite particles known as hadrons. The strong force is mediated by gluons, which “glue” quarks together.
- Figure 3 Quarks
- ⇒ Types of Hadrons:
- 1. Baryons:
- – Baryons are made of three quarks (qqq).
- Example:
- – Proton ([math]\bar{p}[/math] ): uud, with a total charge of +1e.
- – Neutron ([math]\bar{u}[/math] ): udd, with a total charge of 0e.
- – Antibaryons are made of three antiquarks ([math]\bar{qqq}[/math] ).
- Example:
- – Antiproton ( [math]\bar{p}[/math]):[math]u \bar{d}[/math] , with a total charge of −1e.
- – Antineutron ([math]\bar{n}[/math] ): [math]d \bar{u}[/math], with a total charge of
- 2. Mesons:
- Mesons are made of a quark-antiquark pair (q ).
- Example:
- – Pion ([math]π^+[/math] ): [math]u \bar{d}[/math] , with a charge of +1e.
- – Pion ([math]π^-[/math] ): d[math]\bar{u}[/math] , with a charge of −1e.
- Mesons are unstable and decay into lighter particles, often involving leptons or photons.
- ⇒ Quarks Are Never Observed in Isolation
- The strong nuclear force, described by Quantum Chromodynamics (QCD), ensures that quarks and antiquarks are always confined within hadrons:
- – As quarks are pulled apart, the force between them increases.
- – Instead of isolating a quark, the energy required to separate them produces a new quark-antiquark pair, which forms new hadrons.
- This behavior leads to the phenomenon of hadronization, where quarks and antiquarks combine into hadrons after high-energy particle collisions.
- Figure 4 Types of Hadrons
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(e) The Quark Compositions of the Neutron and Proton
- In the Standard Model of particle physics, baryons are composite particles made of three quarks. For the most common baryons, the proton and neutron, their quark compositions are as follows:
- ⇒ Proton (p):
- Quark composition: uud (two up quarks and one down quark).
- Charge of the proton:
- – Up quark (u): [math]+ \frac{2}{3} e[/math]
- – Down quark (d):[math]- \frac{1}{3} e[/math]
- – Total charge = .[math]\left( + \frac{2}{3} + \frac{2}{3} – \frac{1}{3} \right)e = +1e[/math]
- ⇒ Neutron (n):
- Quark composition: udd (one up quark and two down quarks).
- Charge of the neutron:
- – Up quark (u):[math]+ \frac{2}{3} e[/math]
- – Down quark (d):[math]- \frac{1}{3} e[/math]
- – Total charge =[math]\left( + \frac{2}{3} + \frac{2}{3} – \frac{1}{3} \right)e = 0e[/math]
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(f) Using Data to Suggest the Quark Make-up of Less Well-Known Baryons and Charged Pions
- Baryons: Combinations of Three Quarks ([math]qqq[/math] )
- To determine the quark make-up of first-generation baryons, consider the following principles:
- Baryons are composed of three quarks.
- The total charge of the baryon must match the charge provided in the data.
- The only quarks available in the first generation are up (u) and down (d) quarks.
- Figure 5 Quarks
- Here are examples of less well-known baryons and their quark compositions:
- 1. Delta baryons ([math]\Delta^{++}, \Delta^{+}, \Delta^{0}, \Delta^{-}[/math] ):
- – [math]\Delta^{++}[/math]: Composed of uuu (charge [math]+ \frac{2}{3} + \frac{2}{3} + \frac{2}{3} = +2e[/math])
- – [math]\Delta^{+}[/math]: Composed of uud (charge [math]+ \frac{2}{3} + \frac{2}{3} – \frac{1}{3} = +1e[/math])
- – [math]\Delta^{0}[/math]: Composed of udd (charge [math]+ \frac{2}{3} – \frac{1}{3} – \frac{1}{3} = 0e[/math]).
- – [math]\Delta^{-}[/math]: Composed of ddd (charge [math]- \frac{1}{3} – \frac{1}{3} – \frac{1}{3} = -1e[/math]
- 2. Sigma baryons ([math]\Sigma^+, \Sigma^0, \Sigma^-[/math] ):
- – [math]\Sigma^+[/math]: Composed of (charge [math]+ \frac{2}{3} + \frac{2}{3} – \frac{1}{3} = +1e[/math])
- – [math] \Sigma^0[/math]: Composed of (charge [math]+ \frac{2}{3} – \frac{1}{3} – \frac{1}{3} = 0e[/math])
- – [math]\Sigma^-[/math]: Composed of (charge )
- ⇒ Baryons: Combinations of Three Quarks (qqq)
| Particle | Charge (e) | Quark Composition | Reasoning |
|---|---|---|---|
| Proton (p) | +1 | uud | Total charge =[math]\frac{2}{3} + \frac{2}{3} – \frac{1}{3} = +2[/math] |
| Neutron (n) | 0 | udd | Total charge = [math]+ \frac{2}{3} – \frac{1}{3} – \frac{1}{3} = 0[/math] |
| [math]\Delta^{++}[/math] | +2 | uuu | Total charge = [math]+ \frac{2}{3} + \frac{2}{3} + \frac{2}{3} = +2[/math] |
| [math]\Delta^{-}[/math] | −1 | ddd | Total charge = [math]- \frac{1}{3} – \frac{1}{3} – \frac{1}{3} = -1[/math] |
| [math]\Sigma^+[/math] | +1 | uus | Includes the strange quark (s) with charge[math]- \frac{1}{3}[/math] , leading to [math]+ \frac{2}{3} + \frac{2}{3} – \frac{1}{3} = +1[/math] |
| [math]\Sigma^-[/math] | −1 | dds | Total charge =[math]- \frac{1}{3} – \frac{1}{3} – \frac{1}{3} = -1[/math] |
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g) The Four Fundamental Forces or Interactions in Particle Physics
- The universe operates under the influence of four fundamental forces, each with distinct properties regarding the particles they act upon, their range, and their strength. Here is a detailed explanation of the properties and roles of these forces:
- 1. Gravitational Force
- Experienced by: All matter, i.e., all particles with mass (e.g., stars, planets, humans, and particles like protons and neutrons).
- Range: Infinite, meaning it acts over any distance. The strength, however, decreases with distance following the inverse square law ( [math]F ∝ \f{1}{r^2}[/math]).
- ⇒ Comments:
- – Gravity is the weakest of the four fundamental forces but dominates at large scales, such as between celestial bodies (e.g., planets, stars, and galaxies)
- – It is responsible for phenomena such as the orbits of planets, the structure of galaxies, and the motion of objects under free fall.
- – Gravitational effects are negligible at the atomic or subatomic scale because the other three forces are much stronger.
- – Theoretical mediator particle: Graviton (not yet observed).
- 2. Weak Nuclear Force
- Experienced by: All leptons and quarks, and therefore all hadrons (since hadrons are made of quarks).
- Range: Very short (on the order of [math]10{-18} [/math]meters, which is smaller than an atomic nucleus).
- ⇒ Comments:
- – The weak force is responsible for radioactive decay processes such as beta decay, where a neutron decays into a proton, an electron, and an electron antineutrino.
- It is stronger than gravity but much weaker than the electromagnetic and strong nuclear forces.
- – The weak force is essential in processes like nuclear fusion in stars, where hydrogen nuclei fuse into helium, releasing energy.
- – Mediator particles: W and Z bosons, which are massive particles, limiting the range of this force.
- 3. Electromagnetic Force (e-m)
- Experienced by: All charged particles, including protons, electrons, and ions. It is also experienced by neutral hadrons, as they are composed of quarks, which carry charge.
- Range: Infinite, but the strength decreases with distance following the inverse square law ([math]F ∝ \frac{1}{r^2}[/math] ).
- ⇒ Comments:
- – The electromagnetic force is responsible for electric and magnetic phenomena, such as the attraction between opposite charges, the repulsion of like charges, and the behavior of magnetic fields.
- – It is much stronger than gravity at the atomic and molecular scale and dominates interactions between particles in most everyday situations.
- – It plays a critical role in the structure of atoms, where electrons are bound to the nucleus by the electromagnetic attraction between negatively charged electrons and positively charged protons.
- – Mediator particle: Photon (massless, allowing for infinite range).
- 4. Strong Nuclear Force
- Experienced by: All quarks, and therefore all hadrons (e.g., protons, neutrons, and other particles made of quarks).
- Range: Very short (on the order of [math]10^{-15}[/math] meters, roughly the size of an atomic nucleus).
- ⇒ Comments:
- – The strong nuclear force is the strongest of the four fundamental forces and is responsible for holding quarks together to form protons, neutrons, and other hadrons.
- – It also holds protons and neutrons together in the nucleus, overcoming the electromagnetic repulsion between positively charged protons
- – The force becomes weaker at greater distances but is very strong at short distances. Quarks are never found in isolation because of the property of color confinement.
- – Mediator particles: Gluons, which act as the “glue” that binds quarks together.
- ⇒ Comparison of the Four Forces
| Force | Acts On | Range | Relative Strength | Mediator |
|---|---|---|---|---|
| Gravitational | All matter | Infinite | Weakest | Graviton (theoretical) |
| Weak Nuclear | All leptons, quarks, and hadrons | Very short | Stronger than gravity | W, Z bosons |
| Electromagnetic | Charged particles, neutral hadrons | Infinite | Much stronger than gravity | Photon |
| Strong Nuclear | Quarks and hadrons | Very short | Strongest | Gluon |
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(h) Conservation Laws in Particle Reactions
- In particle physics, certain quantities are conserved during interactions or decays. These conservation laws are fundamental principles used to analyze and predict the outcome of reactions. The key conservation laws include:
- 1. Conservation of Charge
- The total electric charge before and after a reaction must be the same.
- Example:
- – Beta decay:
- [math]n \to p + e^- + \overline{\nu}_e[/math]
- – Neutron (n): charge 0
- – Proton (p): charge +1
- – Electron (e−e^-e−): charge −1
- – Electron antineutrino ( [math]\overline{\nu}_e[/math]): charge 0
- Total charge:
- [math]n \to p + e^- + \overline{\nu}_e[/math]
- – Charge is conserved.
- 2. Conservation of Lepton Number
- Leptons have a lepton number of +1, and their corresponding antiparticles have a lepton number of −1.
- Total lepton number (of all flavors: electron, muon, and tau) is conserved in reactions.
- ⇒ Example:
- Electron capture:
- [math]p + e^- \to n + \overline{\nu}_e[/math]
- – Proton (p): lepton number 0
- – Electron (e−): lepton number +1
- – Neutron (n): lepton number 0
- – Electron neutrino ([math]\overline{\nu}_e[/math] ): lepton number +1
- Total lepton number:
- [math]p + e^- \to n + \overline{\nu}_e \\ +1 \to 0 + +1 + 1[/math]
- – Lepton number is conserved.
- 3. Conservation of Baryon Number
- Baryons (such as protons and neutrons) have a baryon number of +1, while antibaryons have a baryon number of −1.
- The total baryon number is conserved.
- ⇒ Example:
- Proton-neutron conversion:
- [math]p + e^- \to n + \overline{\nu}_e[/math](hypothetical reaction)
- – Proton (p): baryon number +1
- – Neutron (n): baryon number +1
- – Positron (e+): baryon number 0
- – Electron neutrino ([math]\overline{\nu}_e[/math] ): baryon number 0
- Total baryon number:
- [math]+1 \to +1 + 0 + 0[/math]
- – Baryon number is conserved.
- 4. Conservation of Quark Number (or Quark Content)
- Quarks and antiquarks are also conserved in reactions, indirectly reflected in the baryon number.
- ⇒ Example:
- – Proton composition: uud
- – Neutron composition: udd
- – In a conversion, one up quark (u) changes into a down quark (d).
- ⇒ Example Reactions and Conservation Laws
- Reaction 1: Beta Decay ([math]p + e^- \to n + \overline{\nu}_e[/math] )
- – Charge: [math]0 = +1 + (-1) + 0[/math]. Conserved.
- – Lepton Number:[math]0 = 0 + (+1) + (-1)[/math]
- – Baryon Number:[math]+1 = +1 + 0 + 0[/math]
- ⇒ Reaction 2: Pair Annihilation ([math]e^+ + e^- \to \gamma + \gamma[/math] )
- – Charge: [math](+1) + (-1) = 0[/math]. Conserved.
- – Lepton Number:[math](+1) + (-1) = 0[/math] . Conserved.
- – Baryon Number: No baryons involved. Conserved as 0.
- (i) Neutrino Involvement and Quark Flavor Changes in Weak Interactions
- 1. Neutrino Involvement
- Neutrinos are neutral particles with nearly zero mass and are only involved in weak interactions.
- They participate in processes such as beta decay, electron capture, and neutrino scattering.
- Example: In beta decay ([math]n \to p + e^- + \overline{\nu}_e[/math] ), the electron antineutrino ensures conservation of lepton number.
- 2. Quark Flavor Changes
- The weak nuclear force is the only force capable of changing the flavor of quarks (i.e., converting one type of quark into another).
- ⇒ For example:
- In beta decay, a down quark (d) in a neutron is converted into an up quark (u), turning the neutron into a proton ([math]dd → uud[/math] )
- This is mediated by the emission of a W-boson, which decays into an electron and an electron antineutrino.