Nuclear and Particle Physics Study Notes
8.130 - Nucleon number and proton number
An atom comprises protons, neutrons and electrons. The nucleus at the centre contains protons and neutrons, hence nucleons, while electrons orbit the nucleus in shells. The proton number Z is the number of protons in an atom, and the nucleon number A is the total number of protons and neutrons. The neutron number is N = A − Z. Nuclide notation is often written in the form ^{A}_{Z}X, where X is the element symbol. This notation encodes the composition of the nucleus: A is the mass number and Z is the atomic (proton) number.
8.131 - Alpha particle scattering as evidence for the nuclear model of the atom
Rutherford scattering provided strong evidence for a nuclear model of the atom. Before this, Thomson’s plum pudding model depicted the atom as a sphere of positive charge with small, evenly distributed negative charge inside like plums in a pudding. Rutherford’s experiment used an alpha source and gold foil in an evacuated chamber coated with a fluorescent material so you could see where the alphas hit the chamber, with a microscope outside to observe the tracks. The observed results contradicted the plum pudding model: most alpha particles passed straight through with little or no deflection, a small fraction were deflected at large angles, and very few were deflected back by more than 90°. From these results it was concluded that the atom has a small, dense, positively charged nucleus at its centre, with most of the atom being empty space.
8.132 - Thermionic emission
Thermionic emission is the emission of electrons from a metal surface when heated so that the free electrons gain enough energy to escape. Electrons can be accelerated by electric fields to increase their velocity, and they can also be accelerated by magnetic fields since the magnetic force on a moving charge is always perpendicular to its velocity. Electron guns use a potential difference to accelerate electrons released from the heated cathode toward the anode, forming a narrow electron beam that travels beyond the anode through a small gap.
8.133 - Particle accelerators and detectors
Electron guns provide beams of relatively low energy for use in particle accelerators. There are two main types of accelerators:
- Linear accelerator (LINAC) – uses an alternating electric field. It is formed by several cylindrical electrodes, known as drift tubes, which progressively increase in length along the accelerator (labelled C1–C4). Adjacent electrodes connect to opposite polarities of the alternating voltage, creating alternating electric fields in the gaps between electrodes.
- Cyclotron – uses a magnetic field and an alternating electric field. The cyclotron consists of two semi-circular electrodes called
"Dees" with a uniform magnetic field perpendicular to the plane of the Dees and a high-frequency alternating voltage between them. Charged particles start at the centre, move in a circular path under the magnetic field, cross the gap between Dees, and are accelerated by the electric field; the radius of their path increases as they are accelerated. The alternating field reverses between gaps, allowing repeated acceleration until the desired speed is reached and the particles exit.
8.134 - Radius of the path for a charged particle in a magnetic field
When a charged particle moves in a magnetic field perpendicular to its velocity, the magnetic force provides centripetal force and the particle follows a circular path of radius r. Equating magnetic and centripetal forces gives
which leads to
where p = mv is the momentum. Thus the radius depends on momentum, charge, and magnetic field.
8.135 - Applications of conservation laws
Conservation laws apply to particle interactions: Charge, Energy and Momentum must be conserved. Example: beta-minus decay n → p + e^- + \bar{ν}_e. Before interaction the total charge is 0. After interaction: charge = (+1) + (−1) + 0 = 0, so charge is conserved. Particle tracks can be observed in cloud chambers or bubble chambers. A bubble chamber is filled with superheated liquid hydrogen; ionised particles create visible bubbles along their paths. In a magnetic field, charged particles trace curved paths, allowing momentum information to be extracted from the radius of curvature.
8.136 - Investigating the structure of nucleons
To investigate an object, waves with a wavelength comparable to the object's size are used. The de Broglie relation links momentum and wavelength by
which shows that higher momentum yields shorter wavelength. Nucleons are extremely small, about 1.6 fm (10^−15 m) in size, so very short wavelengths are required, implying very high energies for the incident particles.
8.137 - Creation and annihilation of matter and antimatter particles
In special relativity mass and energy are interchangeable via
This allows processes at the subatomic level such as:
- Pair production: a photon is converted into a particle–antiparticle pair, which can occur when the photon energy exceeds the total rest energy of both particles; any excess energy appears as kinetic energy.
- Annihilation: a particle and its antiparticle collide and their rest masses are converted into energy, emitted as two photons moving in opposite directions to conserve momentum.
8.138 - eV as units for energy and eV/c^2 as units for mass
The electronvolt (eV) is a unit of energy; 1 eV = 1.6 × 10^−19 J. Common larger units:
- 1 MeV = 1.6 × 10^−13 J
- 1 GeV = 1.6 × 10^−10 J
To convert between joules and MeV/GeV, divide or multiply by the corresponding conversion factors. In energy units, mass is related by E = mc^2, so m = E/c^2, which in MeV/c^2 or GeV/c^2 units gives masses of the order 1.78 × 10^−30 kg per MeV/c^2 and 1.78 × 10^−27 kg per GeV/c^2, with 1 kg ≈ 5.62 × 10^29 MeV/c^2 ≈ 5.62 × 10^26 GeV/c^2.
8.139 - Relativistic increase in particle lifetimes
At relativistic speeds, time dilation makes observed lifetimes longer than the proper lifetime. Muons produced in the upper atmosphere have a rest lifetime ~2 µs, yet a large fraction survive to reach sea level due to time dilation. Time dilation is also relevant in accelerator collision experiments where moving particles exhibit longer lifetimes in the laboratory frame, allowing more time for interactions.
8.140 - The standard quark–lepton model
All particles fit into three broad classes: hadrons, leptons and photons. Leptons are fundamental and do not participate in the strong nuclear force; hadrons are composed of quarks (also fundamental) and experience the strong interaction; photons are the quanta of light. Hadrons are further divided into baryons (three quarks), antibaryons (three antiquarks) and mesons (a quark and an antiquark). The Standard Model contains six quarks: Up, Down, Charm, Strange, Top and Bottom. The Top quark was predicted by symmetry and later discovered experimentally.
8.141 - Particles and antiparticles
For every type of particle there is an antiparticle with the same rest mass and rest energy but opposite charges and quantum numbers. Examples: electron and positron; electron neutrino and electron antineutrino. A table in the original material lists masses, rest energies and charges for these particles.
8.142 - Determining whether particle interactions are possible
A particle interaction is possible only if charge, baryon number and lepton number are conserved. Example: p → n + e^+ + ν_e. Before: Charge = +1, Baryon = +1, Lepton = 0. After: Charge = 0 + (+1) + 0 = +1, Baryon = +1 + 0 + 0 = +1, Lepton = 0 + (−1) + (+1) = 0. All conserved, so the interaction is possible.
8.143 - Particle equations
You should be able to write and interpret particle equations given the particle symbols. For example, the alpha decay of uranium can be written as
Check conservation before and after: Before: Charge = 92, Baryon = 238, Lepton = 0. After: 90 + 2 = 92, 234 + 4 = 238, 0. All conserved, so the interaction is possible.