Cambridge AS & A Level9702

Particle physics

Physics 9702 Chapter Notes

What this chapter covers

Particle physics - Atoms, nuclei and radiationParticle physics - Fundamental particles
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1. Leptons and Hadrons: The Two Families

In particle physics, the 'zoo' of particles discovered in the 20th century is organised into two main families: leptons and hadrons. This classification is based on the fundamental forces they interact with. Leptons, like electrons, are considered truly fundamental particles, meaning they cannot be broken down further. Hadrons, such as protons and neutrons, are composite particles, meaning they are made up of smaller constituents called quarks. The crucial difference is that hadrons experience the strong nuclear force, which binds quarks together and holds the nucleus together, while leptons do not. Both groups are affected by gravity, the weak nuclear force, and, if charged, the electromagnetic force.

Key term

Fundamental Particle: A particle that is not made of any smaller particles and is therefore considered a basic constituent of matter.

Examiner insight

Examiners expect you to clearly state that the defining difference between leptons and hadrons is their interaction (or lack of) with the strong nuclear force.

Common pitfall

A common mistake is thinking that because neutrons have no charge, they are not affected by any forces. They are uncharged, but as hadrons, they are strongly affected by the strong nuclear force.

Fun fact

The word 'lepton' comes from the Greek 'leptos', meaning 'slight' or 'small', because the first leptons discovered were much less massive than the known hadrons.

Worked example 13 marks

Classify the following particles as either a lepton or a hadron:(a) electron,(b) proton,(c) neutron. For each, state one key reason for your classification.

  1. 1

    (a) The electron is a lepton.

  2. 2

    Reason: It is a fundamental particle and does not experience the strong nuclear force.

  3. 3

    (b) The proton is a hadron.

  4. 4

    Reason: It is a composite particle made of quarks and it experiences the strong nuclear force.

  5. 5

    (c) The neutron is a hadron.

  6. 6

    Reason: It is a composite particle made of quarks and it experiences the strong nuclear force.

Recap

  • All particles can be classified as either leptons or hadrons.
  • Leptons are fundamental particles.
  • Hadrons are composite particles made from quarks.
  • Hadrons interact via the strong nuclear force, but leptons do not.
  • Protons and neutrons are hadrons.
  • Electrons are leptons.

Quick check

  1. Which of the four fundamental forces do leptons not experience?1 mark
  2. Is a proton a fundamental particle? Explain your answer.2 marks

2. Leptons: Electrons and Neutrinos

Leptons are a group of six fundamental particles and their antiparticles. For your exams, the most important ones to know are the electron and the neutrino. The electron (e⁻) is a stable, negatively charged particle. Its antiparticle is the positron (e⁺), which has the exact same mass but an opposite, positive charge. The neutrino (ν) is a very unusual particle. It has almost no mass, no electric charge, and interacts very weakly with other matter. It was first hypothesised to explain beta decay. When a nucleus undergoes beta decay, the emitted beta particle (electron) has a continuous range of kinetic energies. To conserve energy and momentum in each decay, another particle must be emitted – the neutrino (or, in beta-minus decay, an antineutrino, ν̅).

Key term

Lepton: A fundamental particle that does not interact via the strong nuclear force, with examples including the electron and the neutrino.

Examiner insight

Marks are often awarded for recognising that a positron is the antiparticle of the electron, having the same mass but opposite charge.

Fun fact

Around 100 trillion neutrinos from the Sun pass through your body every second, but they interact so weakly that maybe only one will interact with an atom in your body in your entire lifetime.

Worked example 13 marks

A positron and an electron are brought close together. Describe what happens and what is produced.

  1. 1

    The positron is the antiparticle of the electron.

  2. 2

    When a particle meets its antiparticle, they annihilate each other.

  3. 3

    Their total mass is converted into energy in the form of two gamma-ray photons, which travel in opposite directions to conserve momentum.

Worked example 23 marks

Explain why the existence of the neutrino was proposed.

  1. 1

    In beta decay, the energy released is a fixed amount for a given nuclide.

  2. 2

    However, the emitted beta particles (electrons) were observed to have a continuous range of kinetic energies, from zero up to a maximum value.

  3. 3

    This appeared to violate the law of conservation of energy. To solve this, Wolfgang Pauli proposed that a second, undetected particle was also emitted, carrying away the 'missing' energy. This particle was later named the neutrino.

Recap

  • The electron and the neutrino are leptons.
  • Leptons are fundamental particles and do not feel the strong nuclear force.
  • The positron (e⁺) is the antiparticle of the electron (e⁻), with the same mass but opposite charge.
  • Neutrinos (ν) are neutral, have very low mass, and interact very weakly.
  • An antineutrino (ν̅) is emitted during beta-minus decay to conserve energy, momentum, and lepton number.

Quick check

  1. State two properties of a neutrino.2 marks
  2. What is the charge and mass of a positron relative to an electron?2 marks

3. Hadrons: Baryons and Mesons

Hadrons are composite particles made of quarks, held together by the strong nuclear force. They are divided into two subgroups based on their quark composition: baryons and mesons. Baryons are particles made of three quarks (or three antiquarks for antibaryons). The most common examples are the protons and neutrons that make up atomic nuclei. Because they are made of three quarks, baryons have half-integer spin (a quantum property you don't need to worry about, but it's their defining feature for physicists). Mesons are the other type of hadron. They are unstable and are made of one quark and one antiquark. Pions (π) are a common example of mesons. Because they contain an antiparticle, mesons are their own antiparticles in some cases, or have distinct antiparticles where the quark and antiquark are swapped.

Baryon Composition: 3 quarks (qqq)

Antibaryon Composition: 3 antiquarks (q̅q̅q̅)

Meson Composition: 1 quark and 1 antiquark (qq̅)

Key term

Hadron: A composite particle made of quarks that interacts via the strong nuclear force, categorised into baryons and mesons.

Common pitfall

Mixing up the compositions of baryons and mesons. A good mnemonic is 'Baryons are Built from three'.

Worked example 13 marks

A particle is composed of three quarks.(a) What class of particle is it?(b) Name a familiar example of such a particle.(c) What fundamental force is responsible for binding the quarks together?

  1. 1

    (a) A particle made of three quarks is a baryon.

  2. 2

    (b) A proton or a neutron is an example of a baryon.

  3. 3

    (c) The strong nuclear force binds quarks together within the baryon.

Worked example 22 marks

A K-meson is a hadron with a quark composition of an up quark and an anti-strange quark (us̅). Is the K-meson a baryon or a meson? Explain your reasoning.

  1. 1

    The K-meson is a meson.

  2. 2

    This is because it is composed of one quark (up) and one antiquark (anti-strange).

  3. 3

    Mesons are defined as having a quark-antiquark structure, whereas baryons have a three-quark structure.

Recap

  • Hadrons are composite particles made of quarks.
  • Hadrons are divided into baryons and mesons.
  • Baryons are made of three quarks (e.g., protons, neutrons).
  • Mesons are made of one quark and one antiquark (e.g., pions).
  • The strong nuclear force holds quarks together inside hadrons.

Quick check

  1. What is the general quark structure of a meson?1 mark
  2. Is a neutron a baryon or a meson? Justify your answer.2 marks

4. The Quark Model

The properties of hadrons, like their charge, are determined by the quarks they contain. There are six 'flavours' of quark, but for your course, you mainly need to know about the up(u) and down(d) quarks. Quarks have fractional electric charges, which is a very strange property! The up quark has a charge of +2/3e, and the down quark has a charge of -1/3e, where 'e' is the elementary charge (the magnitude of an electron's charge). Antiquarks have the opposite charge; the anti-up (u̅) has charge -2/3e and the anti-down (d̅) has charge +1/3e. By combining these, we can construct familiar particles. A proton is a baryon made of two up quarks and one down quark (uud). A neutron is a baryon made of one up quark and two down quarks (udd).

Charge of up quark (u): +2/3 e

Charge of down quark (d): -1/3 e

Proton composition: uud

Neutron composition: udd

Key term

Quark: A fundamental constituent of matter that combines to form hadrons, possessing properties like fractional electric charge.

Examiner insight

Being able to derive the charge of a proton or neutron from its quark composition is a frequently tested skill. Show your working clearly by adding the fractional charges.

Fun fact

Quarks were named by physicist Murray Gell-Mann, who took the name from a line in James Joyce's novel Finnegans Wake: 'Three quarks for Muster Mark!'

Worked example 13 marks

Show that the quark composition 'uud' gives the proton a relative charge of +1.

  1. 1

    The charge of an up quark(u) is +2/3 e.

  2. 2

    The charge of a down quark(d) is -1/3 e.

  3. 3

    The total charge is the sum of the constituent quark charges: (+2/3) + (+2/3) + (-1/3).

  4. 4

    Summing the fractions: 2/3 + 2/3 - 1/3 = 3/3 = 1.

  5. 5

    Therefore, the total charge is +1e, which is a relative charge of +1.

Worked example 23 marks

A sigma-minus particle (Σ⁻) is a baryon with the quark composition 'dds'. The strange quark(s) has a charge of -1/3 e. Determine the charge of the Σ⁻ particle.

  1. 1

    The particle is composed of two down quarks(d) and one strange quark (s).

  2. 2

    Charge of a down quark(d) = -1/3 e.

  3. 3

    Charge of a strange quark(s) = -1/3 e.

  4. 4

    Total charge = charge(d) + charge(d) + charge(s).

  5. 5

    Total charge = (-1/3) + (-1/3) + (-1/3) = -3/3 = -1.

  6. 6

    The charge of the Σ⁻ particle is -1e.

Recap

  • Quarks are fundamental particles with fractional charges.
  • An up quark (u) has a charge of +2/3 e.
  • A down quark (d) has a charge of -1/3 e.
  • A proton's composition is uud, giving it a charge of +1e.
  • A neutron's composition is udd, giving it a charge of 0.
  • The charge of a hadron is the sum of the charges of its constituent quarks.

Quick check

  1. What is the quark composition of a neutron?1 mark
  2. A meson called a pion (π⁺) is made of an up quark and an anti-down quark (ud̅). Calculate its charge.2 marks

5. Beta Decay at the Quark Level

We can now understand radioactive beta decay in terms of quarks and fundamental particles. It's not the nucleus as a whole that decays, but a single nucleon within it. Beta-minus (β⁻) decay occurs when a neutron turns into a proton. At the fundamental level, a down quark within the neutron changes into an up quark. This changes the nucleon from udd (neutron) to uud (proton). This transformation is governed by the weak nuclear force. To conserve charge, a particle with charge -1e must be emitted - this is the electron (the β⁻ particle). To conserve lepton number, an electron antineutrino (ν̅e) is also created and emitted. Beta-plus (β⁺) decay is the opposite process, occurring in proton-rich nuclei. A proton turns into a neutron. Here, an up quark changes into a down quark (u → d). A positron (e⁺) and an electron neutrino (νe) are emitted.

β⁻ decay: n → p + e⁻ + ν̅e

β⁻ quark change: d → u + e⁻ + ν̅e

β⁺ decay: p → n + e⁺ + νe

β⁺ quark change: u → d + e⁺ + νe

Key term

Beta Decay: A type of radioactive decay where a nucleon transforms, mediated by the weak nuclear force, emitting a beta particle and a neutrino or antineutrino.

Common pitfall

In beta-minus decay, students often forget to include the antineutrino, or they write a regular neutrino. Remember: an electron (particle) is paired with an antineutrino (antiparticle).

Worked example 14 marks

Describe the process of beta-minus decay in terms of nucleons and quarks.

  1. 1

    In beta-minus decay, a neutron in the nucleus changes into a proton.

  2. 2

    This occurs at the quark level: one of the down quarks in the neutron (udd) transforms into an up quark.

  3. 3

    The resulting quark combination is uud, which is a proton.

  4. 4

    During this process, an electron (β⁻ particle) and an electron antineutrino are created and emitted from the nucleus.

Worked example 23 marks

The decay of a proton into a neutron is represented by the equation p → n + e⁺ + νe. Show that charge is conserved in this decay.

  1. 1

    Initial charge (from the proton,p) is +1e.

  2. 2

    Final charge is the sum of the charges of the products: neutron (n), positron (e⁺), and electron neutrino (νe).

  3. 3

    Charge of neutron = 0.

  4. 4

    Charge of positron = +1e.

  5. 5

    Charge of neutrino = 0.

  6. 6

    Total final charge = 0 + (+1e) + 0 = +1e.

  7. 7

    Since the initial charge (+1e) equals the final charge (+1e), charge is conserved.

Recap

  • Beta decay is a result of the weak nuclear force.
  • In β⁻ decay, a neutron becomes a proton as a down quark changes to an up quark.
  • β⁻ decay emits an electron and an electron antineutrino.
  • In β⁺ decay, a proton becomes a neutron as an up quark changes to a down quark.
  • β⁺ decay emits a positron and an electron neutrino.
  • Fundamental quantities like charge and lepton number are conserved in all decays.

Quick check

  1. What change happens to a quark during beta-plus decay?1 mark
  2. What two particles are emitted during beta-minus decay?1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. State two differences between a lepton and a hadron.2 marks
  2. A proton is made of the quark combination 'uud'. Use the charges of the up and down quarks to show that the proton has a charge of +1e.3 marks
  3. Explain the role of the neutrino (or antineutrino) in beta decay.3 marks
  4. An anti-neutron is an antibaryon. State its quark composition and determine its charge.3 marks
  5. Compare the properties of an electron and a positron.2 marks
  6. Carbon-14 (¹⁴₆C) decays into Nitrogen-14 (¹⁴₇N) via beta-minus decay. (a) Write a full nuclear equation for this decay. (b) Describe the change that occurs at the quark level within the nucleus.4 marks
  7. A particle called the neutral kaon (K⁰) is a meson with a quark composition of a down quark (d) and an anti-strange quark (s̅). The strange quark has a charge of -1/3e. Deduce the charge of the anti-strange quark and show that the neutral kaon is indeed neutral.4 marks
  8. Distinguish between a baryon and a meson, giving an example of each.4 marks
  9. The Omega-minus (Ω⁻) particle is a baryon with quark composition 'sss'. (a) What is the charge of the strange quark? (b) The Ω⁻ decays into a Lambda (Λ⁰) particle and a K⁻ meson. The Λ⁰ has quark composition 'uds'. Deduce the quark composition of the K⁻ meson.5 marks
  10. Explain why scientists now believe protons and neutrons are not fundamental particles, but electrons are.3 marks

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