3.2.1 Particles

3.2.1.1 Constituents of the atom

Constituents of an atom

Particle	Charge (C)	Relative charge	Mass (kg)	Relative Mass	Specific Charge (\(C \cdot kg^{-1}\))
Proton	\(+1.6 \times 10^{-19}\)	\(+1\)	\(1.67(3) \times 10^{-27}\)	\(1\)	\(9.58 \times 10^{7}\)
Neutron	\(0\)	\(0\)	\(1.67(5) \times 10^{-27}\)	\(1\)	\(0\)
Electron	\(-1.6 \times 10^{-19}\)	\(-1\)	\(9.11 \times 10^{-31}\)	\(0.0005\)	\(1.76 \times 10^{11}\)

Specific charge

• \(\text{specific charge} = \frac{\text{charge}}{\text{mass}}\)
• Unit = \(C \cdot kg^{-1}\)

Nuclide notation

• \(_{Z}^{A}X\)
• \(A\) = nucleon / mass number = number of nucleons (proton + neutron)
• \(Z\) = proton / atomic number = number of protons
• \(X\) = symbol for the element

Isotopes

• Atoms with the same number of protons and electrons but different numbers of neutrons & different atomic masses

Nuclide

• A type of nucleus

Atom and nucleus size

• Size of atom \(\approx 10^{-10} \text{ m}\)
• Size of nucleus \(\approx 10^{-15} \text{ m} = 1 \text{ fm}\)

3.2.1.2 Stable and unstable nuclei

The strong nuclear force (SNF)

• Only affects hadrons
• Acts on nucleons
• Keeps the nucleus stable by counteracting the electrostatic force of repulsion between protons in the nucleus and keeping protons and neutrons together
• Prevents proton and neutron from moving closer or further apart
• Very short range
  • Repulsion for separations less than about 0.5 fm
  • Attraction for separations up to 3 fm (1 fm = \(10^{-15}\) m)
  • Negligible beyond 3 fm
• Exchange particles = pions / gluons
• Much larger in magnitude compared to other fundamental forces
  • 

Unstable nuclei

• Too many protons and / or neutrons
• SNF not enough to keep them stable
• Decay in order to become stable (type depends on the amount of each nucleon)

Alpha decay

• Too many protons and neutrons
• Alpha particle emitted (2 protons + 2 neutrons)
• \(_{Z}^{A}X \rightarrow _{Z - 2}^{A - 4}Y + _{2}^{4}\alpha\)

Beta-minus decay

• Too many neutrons (neutron-rich)
• A neutron changes into a proton
• Fast-moving electron (beta particle) + an electron antineutrino (antiparticle with no charge) emitted
• \(_{Z}^{A}X \rightarrow _{Z + 1}^{A}Y + _{- 1}^{0}\beta + \bar{\nu}_{e}\)

Neutrino (\(\nu\))

• At first scientists believed that only an electron was emitted from the nucleus during beta-minus decay
• Observation of energy levels before + after decay showed that energy was not conserved (some energy was lost)
• Neutrinos were hypothesised for the loss of energy and later observed

Why is collaboration important to making advances in understanding of particle physics

• Results of experiments must be independently checked/validated/peer reviewed before they are accepted/can be confirmed
• Particle accelerators are very expensive and collaboration helps to spread the cost of building them
• Many skills and disciplines are required which one team are unlikely to have
• Lots of data to process so more teams are needed

3.2.1.3 Particles, antiparticles and photons

EM radiation

• Emitted when charged particles lose energy
  • When a fast-moving electron is stopped / slows down / changes direction
  • When an electron in a shell of an atom moves to a different shell of lower energy
• Consists of two linked electric and magnetic field waves that are at right angles to each other and in phase
  • 

The electromagnetic spectrum

• 

Photon model of EM radiation

• EM waves are emitted as short burst of waves in different directions
• Each burst = a packet of EM waves = a photon
• Photons transfer energy and have no mass
• The energy of the photons is directly proportional to the frequency of EM radiation
  • \(E = hf = \frac{hc}{\lambda}\)
  • \(h\) = Planck constant = \(6.63 \times 10^{-34} \text{ Js}\)

Electron volts

• 1 electron volt = the energy transferred when an electron is moved through a p.d. of 1 V
• \(1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}\) (\(1 \text{ MeV} = 1.60 \times 10^{-13} \text{ J}\))

Antiparticle

• All particles of normal matter have a corresponding antiparticle
• Same rest energy and mass as the particle
• All other properties are opposite e.g. charge / strangeness
• Will undergo annihilation with the normal particle if they meet

Types of antiparticles

Particle	Antiparticle
Electron	Positron
Proton	Antiproton
Neutron	Antineutron
Neutrino	Antineutrino

Annihilation

• Where a particle and a corresponding antiparticle meet
• All their mass and KE is converted into two gamma photons of equal frequency moving in opposite directions (to conserve momentum)
• Energy and momentum is conserved in the process
• Minimum energy of a single photon = rest energy of the particle
• 

Pair production

• A photon is converted into a particle and a corresponding antiparticle
• Can only occur when the photon has an energy greater than the total rest energy of both particles
• Minimum energy of a photon needed: \((hf)_{min} = 2 \times \text{rest energy} = 2E_{0}\)
• Excess energy is converted into KE of particles
• 

3.2.1.4 Particle interactions

Four fundamental interactions

Interaction	Exchange particle / gauge bosons	Range (m)	Acts on	Strength
Strong nuclear	Pions (particles) Gluon (quarks)	\(10^{-15}\)	Hadrons	1st
Weak nuclear	W boson (\(W^{+}\) or \(W^{-}\))	\(10^{-18}\)	All particles	3rd
Electromagnetic	Virtual photon (\(\gamma\))	Infinite	Charged particles	2nd
Gravity	Graviton	Infinite	Particles with mass	4th

Exchange particles

• The force carrier for fundamental forces
• Moves between the particles affected by the force and create the forces
• Transfer energy, force, momentum, and (sometimes) charge between the particles experiencing the force
• Each fundamental force has its own exchange particles

The weak nuclear force

• Responsible for beta decay, electron capture and electron-proton collisions
• Exchange particles = W bosons (\(W^{+}\) or \(W^{-}\))
  • Non-zero rest mass
  • Very short range \(\le 0.001 \text{ fm}\) (\(10^{-18} \text{ m}\))
  • Positively or negatively charged

Weak interactions

• Electron capture (electron-proton collisions)
  • Same equation + different exchange particle
  • \(p + e^{-} \rightarrow n + \nu_{e}\)
  • 
• Beta-plus decay
  • \(p \rightarrow n + e^{+} + \nu_{e}\)
  • 
  • 
• Beta-minus decay
  • \(n \rightarrow p + e^{-} + \bar{\nu}_{e}\)
  • 
  • 
• Neutron-neutrino interaction
  • 
• Proton-antineutrino interaction
  • 
• Electrostatic interactions
• 

3.2.1.5 Classification of particles

Deducing whether is strong interaction or not

• Leptons present: must be weak
• Leptons not present: strong or weak
• Strangeness not conserved: must be weak

Classifying particles

• All particles are either hadrons or leptons
• Leptons
  • Fundamental particles - cannot be broken down any further
  • Interacts via weak interaction only
• Hadrons
  • Formed of quarks (fundamental particles)
  • Interact through weak or strong interaction
• Both experiences gravitational interaction and electromagnetic interaction (if charged)

Types of hadrons

• Baryons / antibaryons
• Mesons

Baryons / antibaryons

• Hadrons that are formed of 3 quarks (3 antiquarks for antibaryons)
• Proton is the only stable baryon
• All other baryons eventually decay into protons
• (Neutrons are also baryons)

Mesons

• Formed of 1 quark + 1 antiquark
• Hadrons that do not include protons in their decay products
• Very short life time (annihilate almost immediately) + all unstable
• Pion / \(\pi\) meson
  • The lightest and most stable meson
  • Produced in high energy particle collisions, discovered in cosmic rays
  • Exchange particle for SNF
  • Different charges: \(\pi^{+}\), \(\pi^{-}\), \(\pi^{0}\)
• Kaon / \(K\) meson
  • Heavier + less stable
  • Produced by the strong interaction between pions and protons
  • Eventually decay into pions (many possibilities)
  • Different charges: \(K^{+}\), \(K^{0}\), \(K^{-}\)

Baryon number

• 1 = baryon / -1 = antibaryon / 0 = not a baryon
• A quantum number
• Always conserved in particle interactions

Types of leptons

• Electron (\(e^{-}\))
  • Relative charge = -1
  • Electrons and their neutrinos / antiparticles are the only stable leptons
• Positron (\(e^{+}\))
  • Will eventually encounter an electron and annihilate
• Muon (\(\mu^{-}\))
  • Heavier than electrons
  • More unstable
  • Relative charge = -1
  • Muons decay into electrons by weak interaction: \(\mu^{-} \rightarrow e^{-} + \bar{\nu}_{e} + \nu_{\mu}\)
    • 
• Antimuon (\(\mu^{+}\))
  • Antimuon (\(\mu^{+}\)) decays into positions: \(\mu^{+} \rightarrow e^{+} + \nu_{e} + \bar{\nu}_{\mu}\)
• Neutrinos (\(\nu_{e}\), \(\nu_{\mu}\))
  • Negligible mass & 0 charge
  • The most abundant leptons in the universe
• Tauons and & their neutrinos (not required to know)

Lepton number

• Gives the number of leptons
• 1 = lepton, -1 = antilepton, 0 = not a lepton
• Conserved during reactions

Strangeness

• A quantum number
• Reflect the fact that strange particles are always created in pairs
• Explain why some particle interactions take place more slowly than others / do not occur at all
• Always conserved in strong interactions
• Change by 0, +1 or -1 in weak interactions

Strange particles

• Particles which are produced by the strong nuclear interaction but decay by the weak interaction
• Strange particles are created in twos
• e.g. kaons (decay into pions through the weak interaction)
• Assume all others are non-strange particles
• Particles with strange quarks have long lifetimes

Investigating particle physics

• Particle accelerators may be built
• These are very expensive + produce huge amounts of data
• Scientific investigations rely on collaboration of scientists internationally

3.2.1.6 Quarks and antiquarks

Quarks

• Baryons and mesons are composed of quarks
• Quarks feel the strong force
• Quarks are always found in pairs or triplets

Combination of quarks and antiquarks in baryons / antibaryons

Particle	Combination	Baryon number	Strangeness
\(p\)	\(uud\)	\(1\)	\(0\)
\(n\)	\(udd\)	\(1\)	\(0\)
Antiproton	\(\bar{u}\bar{u}\bar{d}\)	\(-1\)	\(0\)
Antineutron	\(\bar{u}\bar{d}\bar{d}\)	\(-1\)	\(0\)
\(\Sigma^{+}\)	\(uus\)	\(1\)	\(-1\)
\(\Sigma^{0}\)	\(uds\)	\(1\)	\(-1\)
\(\Sigma^{-}\)	\(dds\)	\(1\)	\(-1\)

Combination of quarks and antiquarks in mesons

Particle	Combination	Charge (e)	Strangeness	Baryon number
\(\pi^{0}\)	\(u\bar{u}\) or \(d\bar{d}\)	0	0	0
\(\pi^{+}\)	\(u\bar{d}\)	+1	0	0
\(\pi^{-}\)	\(\bar{u}d\)	-1	0	0
\(K^{0}\)	\(d\bar{s}\) or \(\bar{d}s\)	0	\(d\bar{s} = +1\), \(\bar{d}s = -1\)	0
\(K^{+}\)	\(u\bar{s}\)	+1	+1	0
\(K^{-}\)	\(\bar{u}s\)	-1	-1	0

Strangeness of particles

Strangeness	Particles
\(-3\)	\(\Omega^{-}\)
\(-2\)	\(\Xi^{-}\), \(\Xi^{0}\)
\(-1\)	\(\Lambda\), \(K^{-}\), \(K^{0}\), \(\Sigma^{+}\), \(\Sigma^{-}\), \(\Sigma^{0}\)
\(0\)	\(p\), \(n\), \(\pi^{+}\), \(\pi^{-}\), \(\pi^{0}\)
\(1\)	\(K^{+}\)

Neutron decay

• Decay into proton as neutrons are baryons
• A down quark changes to an up quark
• \(n \rightarrow p + e^{-} + \bar{\nu}_{e}\)

3.2.1.7 Applications of conservation laws

Properties conserved in particle interactions

• Energy and momentum: always
  • Reactants rest energy < products rest energy = reactants KE > products KE
• Charge: always
• Baryon number: always
• Electron lepton number: always
• Muon lepton number: always
• Strangeness: only in strong interactions
• All conservation laws obeyed = the interaction is possible

β decay

• β- decay
  • A neutron in a neutron-rich nucleus will decay into a proton
  • A down quark changes to an up quark
  • \(n \rightarrow p + e^{-} + \bar{\nu}_{e}\)
• β+ decay
  • A proton in a proton-rich nucleus changes into a neutron
  • An up quark changes to a down quark
  • \(p \rightarrow n + e^{+} + \nu_{e}\)